H1B transfer information to current H1B employer is not sent
Your current employer will not get to know about your H1B transfer on its own.
USCIS does not send any information explicitly to notify about transfers.
H1B transfer petition is denied - Employer B
If your transfer petition is denied, you cannot work with Employer B. If your current H1B from Employer A is still valid, you can keep working with them (or go back to them if you already moved to Employer B, based on transfer receipt number).
Employer A should not revoke H1B petition
Make sure your Employer A does not REVOKE your H1B petition when you move to Employer B. This will help in future if your Transfer gets rejected/denied and you want to go back to Employer A.
Possibility of going out of status after H1B transfer denial
If You move to Employer B based on H1B transfer petition’s receipt number (with result still pending) and Employer A revokes your H1B, you will be OUT-OF-STATUS as soon as the Employer B’s transfer petition is denied.
My advice - Do not Move without H1B transfer approval
My personal advice will be to keep working with Employer A until Employer B’s petition is approved to avoid any issues later.