Maybe the OP's situation is the same.
In fact, in such cases, you don't even need a new visa stamp for the transferred H1B. As long old H1B stamp has not expired, you can present this H1B along with the approved transfer petition and they will let you in.
This is just my understanding of the process and does not constitute legal advice. I am not an immigration attorney or any such. Just a technology guy -:)
Even if it were some sort of H1B transfer, I believe by leaving the US he might have abandoned his H1B. So I think the OP better get his immigration status verified by his new employer, because the last thing he wants to do is get a 10 year ban at the border.
Basically, you must get a brand spanking new H1B to start a new job. However, if you have already recently gotten a H1B, then you can skip the quota, and get it approved pretty much immediately. This is commonly referred to as a "transfer" even though it is not technically a transfer.
I do not understand how could he quit his job and search for another job for 3 months using the same H1B.
I might be missing something here.
Technically, if you lose your H1B job, you're out of the country right now. However, in practice there is some leeway, though lawyers differ on what they expect USCIS will let you away with (there seems to be some consensus on "10 days" though).