I've fixed rotary vac pumps by pulling the lid, driving out the remnants of the stock check valve, tapping the lid to 1/8 NPT making sure to chamfer the edges so the vanes don't catch and installing one of these check valves. Be sure that when you tap the lid you don't tap so far that the check valve will protrude past the lid. I then used a 1/2" barb fitting (I cut it off a fitting I had on hand), tapped it to 1/8"NPT and attached it to the check valve. It works perfectly and is an upgrade from the stock piece in being much more robust.
...BTW your Bieber avatar is awesome.-Malone
I think the picture posted doesn't have a check valve.