No Title
If you have H1 approval which is valid and not cancelled by your company, then you should also have a stamp in the passport. If there is no stamp and your H1 is still valid, then you may/may not be asked questions at the port of entry. To avoid this risk, whereever you are, it\'s a good idea to have your H1 Visa stamped in your passport. If you are out of country, when you come to US, if there is no issue of your H1 visa (ie. if everything is okay), you will be given a new I-94 at the port of entry in US, depending on your H1 Visa validity.Don\'t get misunderstand with the I-94 on your H1 Visa front page. Along with that when entering US, you will be given one more, with an entry stamp and validity to remain in US, which will be attached to your passport.
Hope you got a good idea. Safeside you can show them your I-485 reciept if you think, some issue may arise at the port of entry.
No need to have Adv parole, if you are not using EAD to work in USA.(instead of H1). Good luck.