Can I transfer my H1B to a company B before start working for company A?

I would appreciate your advise in a situation decribed below:
In the beginning of this week I have received a hard copy of approval for my H1B stamped I got email from a manager from the company A that the position is not available anymore and they cannot hire me.

1) What can I do in this situation with my [H1B]( approved? Can I transfer to another company on that petition even if I did not start working for company A?

2) If yes, what are the main steps of that process? Does a new employer have to pay any additional fees if it wants to be my sponsor? How long is takes to have a new sponsorship approved?

3) Do I have any deadline to find a new sponsor?

4) What about salary and job description - do salary and responsibilities have to be the same as those mentioned in original application submitted by company A?

Thank you in advance!