Strop, 25, is in his third stint with the Rangers this season and made one appearance coming on June 1 when he tossed a scoreless inning against the White Sox. He has spent the rest of the season with Oklahoma City, where he has gone 1-1 with seven saves and a 2.79 ERA in 24 relief appearances.
Molina was added to the 40-man roster on Thursday with the trade becoming official, but will not be added to the 25-man roster until Friday with fellow catcher Max Ramirez expected to be optioned to Oklahoma City.
But Ron Washington had nothing but positive things to say about Ramirez, who hit .217 with two homers and eight RBIs in 28 games and improved his defense behind the plate.
"Max should be very proud of himself," Washington said. "And everyone who had their hands on him should be proud of the progress he's made. I know we're proud because of what he's done with the pitching staff and the time he's put in to learn the system."