[coolsank]

IANAL, but once your new firm applies for the new H1B petition (the H1B transfer is technically not a transfer, but a new H1B petition itself that is not subject to the cap), and you receive the receipt of your notice (usually take 2-3 weeks), you can start working for your new firm. There's no requirement to wait until it gets approved.

[proberts]

That's correct and you can even start working for the new employer upon confirmed delivery of the H-1B petition to USCIS< But there's risk with this of course. Unless there's a compelling reason, it makes sense to wait until the petition has been receipted in by USCIS and the filing fee checks cashed. But also note that you do not need to start working upon receipt; you can remain in valid status in the US while the petition is pending and only start working after it is approved.