I haven't done it, but I imagine it would not be difficult.
If I were doing it, I'd first remove the non-working one from the trailer, making notes/taking pictures of all the connections. I'd also measure the converter's dimensions, and the space available where it was mounted.
Once I had all that information, I'd look for a converter that was similar. Most places you buy from list the dimensions and they generally have pictures of the connection points. If they don't, look elsewhere. These things might also come with an owner's manual that you can download before ordering. The manual should give you the information you need.
- Jack