Question on: AP and H1B transfering

Hello Folks,

I have get my NIW approved and I-485 in pending. I ted my NIW and I-485 when I was in my previous employer.

I has used Advanced Parole recently to get back to the States. I am on the 6th year of my H1B.

Since I have I-140 approved and I am qualified to get 3 year H1B extension. Can I get my H1B transfered to a new employer [university]? The research is same. The title is different.
Will I be able to get a new H1B if I switch to the new employer?

One more question on the I-485:
The title when ted the GC petition was Sr. Research Associate. The current title is research scientist. The future will be research assistant [different school systems have different rules].

Thanks.

fishlet