Is the prayer of one who caught the last رکعة with the Imam, then prayed two رکعات after the Imam’s Taslim, then followed it with a final رکعة and a prostration of forgetfulness, valid?

If you doubt the number of rak'ahs (units of prayer) you caught up with the Imam, then build upon the minimum (one rak'ah) and complete your prayer. Then, sit for the tashahhud (testification of faith) in the second rak'ah (which is the first of your missed rak'ahs being made up), and perform the prostrations of forgetfulness (sujud al-sahw) before the taslim (salutation of peace), acting upon the hadith of Abu Sa'id, may Allah be pleased with him. Your prayer is valid if you completed three rak'ahs and performed the prostrations of forgetfulness. You are permitted to verify the number of rak'ahs by observing the prayer of the person next to you.