I am on the same boat. There are two sequential steps for a transfer:
1>LCA(labor condition applicatoin)
2>H1b Transfer
The first step takes about a week or so from online submission to approval;
After LCA is certified, the you can submit H1b transfer. You can start
working for the new employer immediately after they submit the transfer by
law.
I would say 4 weeks seems to be sufficient.
