Well first of all I want to say that Budgies are probably the toughest species of parrot to convert from an all-seed diet to a pellet diet, or pellets at all...I've had Budgies since I was 6 and grew-up with dozens of them in the house at any given time (my mom and grandma bred and hand-raised many different species of Budgies/Parakeets). Often the breeder-Budgies that we would bring in as adults were on all-seed diets for their entire lives up until that point, and converting them to at least a partial-pellet diet was a challenge, to say the least...So I feel your pain.
***The first thing that I would tell you to try, if you haven't already, is the Harrison's conversion-plan that Gail has posted the link to above. It is by-far the best diet-conversion plan/schedule I've ever seen, and we've seen it work for many, many people here that Gail has provided the information to. I would always make the Harrison's conversion-plan the first thing I would try if my goal was to convert the bird from an all-seed diet to a mostly-pellet diet. Thank you Gail for once again posting the link to the Harrison conversion-plan, lol, whenever I read a thread about how to do a diet-conversion I immediately go to post about you and the Harrison's plan, if you don't beat me to it first...It's seriously that good a plan.
***Now, that being said, what exactly is your (or your CAV's) end-goal here? Are you looking to get him off of seeds completely and have him eat nothing but pellets (not recommended), or are you simply trying to make pellets the main staple of his diet, and then have a healthy, fortified, low-fat, and varied seed-mix be included as a daily supplement to the pellets? And does your Budgie eat fresh veggies and/or fruit on a regular basis right now?
I wouldn't ever totally exclude seeds from your bird's diet, in-fact, parrots need to eat seeds every day to stay healthy, both physically and psychologically. Their bodies are designed for them to mainly eat and process seeds, grains, nuts, and plant matter (obviously not pellets, lol), mainly their GI Tracts, and without them eating seeds every day they can actually develop several different Gastrointestinal health issues, not to mention the psychological issues this can cause. Pellets are healthy in the sense that they are specifically designed to to provide them healthy nutrition and eliminate the bad stuff, such as fat, sugar, salt, etc., but unfortunately pellets do nothing for parrots beyond that. So while pellets should ideally be the main staple of their diet, or at least one of the staples of their diet, seeds needs to also be a part of their every-day diet. I know lots of people and have seen many people here who say that they only give their parrot any seeds at all as an "occasional treat", and then say something like they only give their bird "a teaspoon of seed-mix once a week for their treat"...I'm sorry, but that's just wrong, and lots of board-certified Avian Vets totally agree.
The key here is WHAT seed-mix are you feeding your bird, and is it healthy, fortified, low-fat, high-protein, and varied?...What brand/type of seed-mix have you been feeding your Budgie since you brought him home?
The way I would start this process is not to just eliminate or necessarily even immediately reduce the seed-mix from your Budgie's diet and just give him pellets. Rather, I would decide what pellet you want to get him eating and then, if necessary, I would switch him over to a seed-mix that again is healthy, fortified, varied, low-fat, and that provides him with all of the necessary vitamins, minerals, amino acids/digestive enzymes, etc. that he needs to stay healthy. And I would switch him over to that seed mix first, before doing anything else. They typically like whatever seed-mix you give them, so that's the easy part, and this is step #1 in getting him on the road to a healthy diet.
After you get him on a very healthy, varied seed-mix daily, then you can start working on slowly and gradually incorporating the pellets into his daily diet WITH the seed-mix. Budgies are so tough to get eating pellets, which is the result of a lot of different factors, but with Budgies it can have a lot to do with the size and the shape of the pellets. But again, at this point you don't want to yet start replacing the seed-mix with the pellets, but rather add the pellets to his seed-mix.
I've never fed LaFeber pellets, only the Nutriberries as a treat, but I've seen them before, and if I remember correctly they are a brown color and are long and shaped like alfalfa pellets or rabbit/hamster pellets, instead of being round, is that correct? Have you tried to crumble the pellets up, or break them into very small pieces for him? Some Budgies like them soaked, some don't, that's usually not the way to go when trying to introduce them to him because if he likes them that way then he can end-up only eating them if they are soaked. But Budgies like very small pieces of food, even their seeds need to be small (they don't even tend to like to eat whole sunflower seeds because they are too large), so I always feed Budgie pellets that are extremely small...Think about it this way: Look at the size of the seeds he usually eats and likes to eat, and then make sure that none of his pellets are any larger than those seeds. Anything larger can be overwhelming for them.
The other issue I've seen some Budgies have with pellets, as silly as this sounds, is that they get extremely frustrated because they can't shell them! Seriously. I first realized this years and years ago when I was working on hand-taming a Budgie that was a former breeder of my mom's who she loved so much (he was gorgeous and very smart, believe it or not, and friendlier than most of the breeders). So after she retired him she wanted to see if he could be incorporated into the house as a pet, rather than living out his days in the outdoor aviary with the rest of the retired breeders. He loved pea-pods, so I was using them as his training treat but I ran out, and all I had as far as treats at the time were sunflower seeds (unshelled). So I gave him a sunflower seed that was already shelled, and he was excited about it, he took it from my hand, but he had absolutely no idea what to do with it. He actually "shelled-it", at least that's what he thought he was doing, by literally removing that thin, clear "skin" that is around sunflower seeds. He did it to every one I gave him. I was telling him "You can just eat it! You don't have to do that!", but nope, he just absolutely had to take the "shell" off of every seed...So a lot of the time when they won't eat pellets, it's simply because they don't know HOW to eat pellets, as they have no shell to remove! Something that has worked for me when this is the issue is first breaking apart the pellets/crumbling them and making sure that they are no larger than the Budgie's regular seeds, and then first thing in the morning giving them a very small amount of their seed mix in their bowl, with about a quarter of the total mix being the crumbled pellet pieces. Make sure that when you mix them in that all of the seeds and the pellet pieces are just about the same size. The reason you want to make the overall amount of food small when you first try this is that you want to be able to see exactly what he ate and what he didn't eat the first time you try this, so only start out by feeding him a total of maybe 2 tablespoons of food, with only 1/4 of the total being the crumbled pellet pieces and the other 3/4 being his regular seed mix. Let him eat until he walks away from the bowl, and then go back and remove the bowl and see exactly what he's left behind and what he's eaten. If he's eaten only the seeds and none of the pellet pieces, then you know that the size isn't the issue. If he's eaten everything, or he's eaten most all of the pellets with very few pieces remaining, then you know that the size was the issue!
If this doesn't work, you may need to consider that the LaFeber pellets aren't what is going to work for him, and you need to try another brand of Budgie pellets. There are a lot of very healthy pellet mixes out there (less for Budgies than larger parrots, but still a lot of great pellets out there)...Zupreem makes a great natural Budgie Pellet, as do Tropican (this is what I feed my Budgies and they love it), Harrisons does, and there are many more, but those are the ones that I've had success with and that are very healthy for them...So if you can get him eating a main-staple of pellets with a healthy, fortified, varied seed-mix as a supplement to the pellets, along with fresh veggies every day, then he'll be good to go. But in the meantime he still needs to eat, lol, so if there is an issue with his Liver or any other health problems due to the seed-mix he has been eating, then again, it's not at all about eliminating the seeds from his diet, but rather about switching him to a much healthier, varied, low-fat seed-mix.