Is it permissible for a traveler, if he prays behind an Imam who is completing the prayer, to shorten his prayer by praying two rak'ahs with him, then saluting and leaving?

If a traveler prays behind a resident imam, he must complete the prayer with four rak'ahs, whether he caught the entire prayer, one rak'ah, or less; because the imam is there to be followed. Also, Ibn Abbas said to someone who asked him about the prayer of a traveler behind a resident: "That is the Sunnah," and due to the action of Ibn Umar. So, if a traveler joins the prayer while the imam is in the last two rak'ahs, he must, after the imam's taslim, stand up and complete what he missed to pray four rak'ahs, based on the general statement of the Prophet, peace and blessings be upon him: "What you catch, pray, and what you miss, complete." And whoever previously prayed two rak'ahs behind a resident imam in such a case must repeat those four-rak'ah prayers.