non cap H1B transfer

[Sam_b]

Hi

I am working on H-1B for non profit organization(npo). This H-1 type has no cap on it.
If I wish to change my job to a company which is not a npo, is it possible to transfer the H-1B and can I start working immidiately once I file the petition. Or is there any problem in transferring h-1 from non cap to cap type of H1

Thanks