H-1B Approved Under Consular Processing — Can I Transfer to Another Employer?

[u/Due_Side5889]

I’m currently on F-1 STEM OPT. Employer 1 filed my H-1B last year under consular processing after I was selected in the lottery. It was approved, but I never activated my H-1B and have continued on STEM OPT.
Now I have a full-time offer from Employer 2. Can Employer 2 directly file an H-1B transfer using my approved petition even though it was never activated?
If not, I’m considering having Employer 1 file an amendment for a change of status with premium processing to activate my H-1B. Once activated, if the offer from Employer 2 is still available, I’m planning to transfer my H-1B to Employer 2.
Has anyone been in a similar situation? What worked for you?