Let's say Aharon missed Shacharis. He needs to pray Shemoneh Esrei twice by mincha time to make it up, which is called "tashlumin" (תשלומין). (OC 108:1)
Now, Aharon can put on tefilin at any point in the day (though he won't do so at night).
Is there any reason to put them on specifically when he davens (prays) his tashlumin (the second prayer)? After all, that prayer is a stand-in for Shacharis.
I'm looking for an answer that says "this sefer says" or the equivalent; I'm also capable of saying "hey, can't hurt, right?"