Possibility of h1b transfer from non profit to Non profit.???

Hello, Currently I am working in a research institute. They’re currently filing my h1b as non-profit category. I also got offer from another non-profit institute which is a better position than current one. I want to move there.

My question is:

Once I get my non-profit h1b from my current research institute, Can I able to transfer it to new non-profit institute? What’s the process?

Please advise.

Thanks in advance.