I have a single door Frigidaire professional series PLRU1778ES6. It's not cooling properly as the title says. If I adjust the thermostat I can get it to run when it gets about 50 degrees it cuts off. A little bit of help please had a repair guy come out charge me $50 put some freon in because it was a bit low. Did not fix the problem.....

Here are your parts
Parts for Frigidaire PLRU1778ES6 Refrigerator - AppliancePartsPros.com

By "cuts off" I am assuming that you mean that the compressor and it's fan shut off.
Also that when it does shut off it does not start short cycling which would be an indication that the compressor is overhaetig.

If you can re-start it by adjusting the control thermostat up and/or down, then that is the most likely culprit.

[COLOR="Blue"]So how would I go about testing it to make sure that is that problem?[/COLOR]
My first post was the test.
There are two parts that can cause your problem the thermostat or the defrost timer. The thermostat is the most likely and a fairly common problem.
If moving the thermostat does not work then you turn the defrost timer cam to see if the unit starts. But one thing to not is that the unit may be in a legitimate defrost cycle which it does every 8 hours or so.

[COLOR="Blue"]If it is what part would I have to replace to fix it?[/COLOR]
Yes you have to replace it.

One other possibility is a bad connection but that will be difficult to find and is also very very rare.