I have a threadless fork on my 50cm frame that needs to be replaced because it is bent. I have looked around for a fork that might work and have found the same fork, only this one is threaded, but it is coming from a 48cm frame (same model frame as mine), but with I presume has a shorter headtube. I am aware I will need a threaded headset and stem, but my question is will this threaded fork from a smaller frame work with my larger frame? I am not familiar of the workings of a threaded system so please excuse my rookie question.

The only way to know is to measure it. Threaded headsets vary in stack height from about 32mm to 40mm depending on brand and model. As long as the steer tube of the donor fork (measured from the crown race seat to the top of the steer tube) is at least 32 - 40mm longer than the head tube of the recipient frame you should be able to make it work. Longer is better -- you can always trim the steer tube if it's too long but if it's too short you're SOL.