The fact that he oversyed his visa will not effect his application if he is marrying a US citizen. However, if under hte J visa he was subject to hte 2 year home residency requirement he may have to apply for a waiver.
Speak with an attorney, it will all hinge on whether his J1 visa is subject to the 2 year residency requirement. Click the link below for more information on the J1 residency requirement, my firm handles these types of cases.
Law Offices of Nicklaus Misiti
212 537 4407
Legal disclaimer: The statement above is general in nature, as not all the facts are known. You should retain an attorney to review all the facts specific to your case in order to receive advise specific to your case. The statement above does not create an attorney/client relationship.
A J-1 needs to be reviewed for a two year residency requirement or waiver if warranted to initiate AOS under One Stop filing without leaving the U.S. That could be done only at the office by an experienced immigration attorney.
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If the J1 is not subject to the 2 year foreign residency requirement, he should not have a problem becoming a permanent resident of the US. If it is subject, he may only apply after a waiver of that requirement. However both of you should consult with an attorney together to understand the full process.
Dhenu Savla, Esq.
This answer does not create an attorney-client relationship and is not meant to be relied upon as legal advice.