would my fiance be able to stay in the US after we get married, while we are waiting for his papers even though his H2B visa is about to expire?

Dear Madam, Thank you for posting your question.  Congratulations on your planned marriage. Yes, so long once you file your paperwork prior to his visa expiration, he is eligible to reman in the US legally during the period of "authorized stay" pursuant to his application for permanent residence.  I wanted you to know that for immediate relatives (your fiance would become one once you get married), US immigration laws do not penalize those who submit their petitions even after their visa had expired.  The most important element in such applications is that the alien had been "admitted or paroled" into the US.  An H-2B visa recipient is certainly admitted.  But having said that I would highly advise you to file your petition and application prior to his visa expiration in order to avoid any immigration complications. Please let me know if you have any additional questions or comments.  The Law Firm of Shihab & Associates, Co., LPA 1-877-479-4USA gus@shihablawyers.com