What is the ruling on someone who forgot the pre-salutation prostration (sujud al-qabli) and remembered it after the taslim?

Whoever forgets the prostration of forgetfulness (sujud al-sahw) whose place is before the salutation (taslim), then remembers it a short time after the salutation, he should perform the prostration of forgetfulness. He should say "Allahu Akbar" when prostrating and rising, and perform two prostrations, then recite the tashahhud and give the salutation. However, if a long time has passed or something that invalidates the prayer has occurred, he should not prostrate, and his prayer is valid.