I am on H4 Visa got H1B VISA in March 2011, I got I797B w/o I-94, which needs stamping before starting work, but now my employer is not providing enough documents for stamping. Meanwhile I got an offer from other company and they said that they are ready to transfer my H1b,and also they are saying that once H1B transfer is done, I don’t need to go for stamping as I will get new –I797A (WITH i-94). Also I can start working once WAC number is received. For the record, I don't have any paystubs / W2 form, as I have not yet started working for my current employer.

-My question is:
1) Is it possible to transfer visa on I-797B?
2) Is it possible that due to transfer process I will get change of status?