Hello, and welcome to the Parrot Forums family!
Hmmm... There are behavior modification and training tactics to try, but if your little guy has been screaming nonstop every waking hour for a month now, the very first thing I'd do is take him in to see a certified avian vet (the certified part is important. A certified avian vet might catch subtle things that a regular exotics vet might not) to rule out any medical issues. He might be screaming due to physical discomfort or even pain.
Take him in even if he seems fine. Birds instinctively try to hide illness or weakness, as predators target the weak as easier prey.
Also, make sure that you are feeding him enough. He could be screaming out of hunger. Were you able to confirm with his prior parront how much he was fed? Was he also a screamer there?
If he checks out okay medically, and his food amount seems to be on point, you can begin by properly training him to target and step up. Here are videos on both:
Stepping up: [ame="https://youtu.be/GIaDDSeZKnI"]Parrot Training Workshop Live Demo - Step Up Training with a Macaw - YouTube[/ame]
Target Training: [ame="https://youtu.be/HaOicTtwIZo"]Beginners guide to target training parrots - YouTube[/ame]
Both of these are very important. They form the foundation of an interactive relationship with your bird. The best time for this training is between meals, when your bird is at his hungriest. Note that I'm not advocating the withholding of food for the purposes of training, as I abhor that method. Rather, I'm suggesting strategically timed training.
This is assuming a meal schedule that revolves around specific, designated meal times, whether two or three times a day, rather than free-feeding. With my birds, it's 2x a day, with a nighttime snack before bedtime. So my optimal training time is maybe a half hour to hour before dinner, when those treats will be especially tempting. Training should then last anywhere between 5-20 minutes per session, depending on your lil' guy's attention span. Never go for longer than his eagerness can maintain, as he'll lose interest. Just like show biz, keep him wanting more!
Be lavish with your praise, and use their favorite foods for treats. Stuff that he can't get at his regular meals. With my ekkies, I just use nuts broken into smaller pieces. (Not so big as to fill them up quickly, nor so small as to be unworthy of the effort. Aim for "Just right", Goldilocks style.)
You may find that improving your interaction with him cuts down on the screaming in and of itself, as the screaming may just be an expression of boredom. If not, there are methods you can engage to help bring the screaming down to more tolerable levels. You just want to work on establishing a bit of a bond between you, first, as most of the methods used against screaming rely upon the bird actually enjoying your company. He needs to begin associating you with fun time! And the training described above will take you far in that direction. As intelligent birds, parrots enjoy learning new things. Mental stimulation is key. You can help the association along with shameless bribery as well. Nothing says love to a parrot like the presentation of a beloved treat item.
Once the association has been made between your presence and heavenly treats, here is a link to scream extinction methods:
Barbara's Force Free Animal Training Talk: Stop your Parrot from Screaming for Attention
Keep in mind, it's unrealistic to expect a perfectly quiet bird. It's absolutely normal for a bird to make occasional flock calls when you are out of the room to check on you. Or to have set times during the morning or evening when they like to test the range of their singing voices. These methods are set to address screaming on the level that you have described in your post. It might take some time, as some birds are more stubborn than others, but you'll get there. Persistence is key. Persistence and patience.