H4 to h1 but always remained on valid h4

Please help me with below situation.

Currently on h4. I had my h1b petition approved last year under consular processing (no i94 received because travelled out of country during processing). My employer didjt find me a project because i was on H4 and they never filed COS for me. So from last 7 months i have h1 petition approved but always remained on H4. Now new employer is willing to give me a job and he is ready to transfer my existing H1 under cap except. Below are my doubt.

Can he change or transfer my h1 to his company (with no pay stubs because i was always on H4) with cap exempt.



experts please suggest and provide your inputs