H1B Transfer before October

I have a valid H1B approved but it goes into effect in October. Currently I am on OPT till December and STEM OPT extension for another 2 years. My contract with client for employer A ends in June this year and employer A agrees to keep me on unpaid leave until July. Is H1B transfer possible in this case? Can my original petitioner request for H1B withdrawal? What is the best thing to do in this situation?

Transfer aka change of employer petition can only be filed if the beneficiary is already on H1B status.
In your case a new employer can file a cap-exempt H1B petition based on already approved H1B however it won’t start till 1st October as it is first time H1B.
The original H1B sponsoring employer will withdraw the H1B after 1st October once they know that you wont be joining them.