What should one do who prayed Jumu'ah standing due to the extreme crowdedness of the mosque, and did not bow (rukū') or prostrate (sujūd)?

If someone is unable to perform the bowing (rukūʿ) and prostration (sujūd) in the Friday prayer due to severe crowding, scholars differ on whether he has caught the Friday prayer. Some believe that he has caught it and should pray two rakʿahs after the crowd disperses. Others believe that he has not caught it and must pray four rakʿahs. If the person proceeds with his initial intention (iḥrām) and prays four rakʿahs after the crowd disperses, this is sufficient for him, just as it would be sufficient if he prayed two rakʿahs according to the opinion that he caught the Friday prayer. However, if he makes the salām with the imam without completing the prayer, the Friday prayer is invalid, and he must repeat it as a Dhuhr prayer of four rakʿahs if he cannot attend another Friday prayer. It is incumbent upon one who is unable to prostrate due to crowding to prostrate on the back or foot of the worshipper in front of him if possible.