Her is the response from my University Officer

Here is response from my University Officer.
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There is conflicting information out there about this issue. There is a
memo indicating that if you return on Advance Parole and continue to
work for the same employer, you should be able to extend your H-1B
status. A memo however does not carry the same weight as the
regulations. I personally have never filed an H-1B extension
application for someone who has returned on AP, but I understand that
there are those out there who want to try in the future.

The safest thing I think you can do if you are traveling under AP is to
also have an EAD (Employment Authorization Document) to work when you
return. We can then attempt to extend your H-1 status, but if for some
reason it is denied, you would still have the EAD to fall back on.
Another option would be to try to apply for an H-1B visa while you are
overseas and return as an H-1. I think those two options are the safest
things to do.

If you travel on AP, you should not need anything from the University.
If you travel and apply for the H-1B visa, let me know because I will
need to prepare some documents for you.
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