It would help to understand how you actually want to use these structures, but here's my initial suggestion. You don't need Module and you don't need Print. Try something like this:

angsym2[n_, s_, l_, j_] :=
 With[
  {lsym = Switch[l, 0, "S", 1, "P", 2, "D", 3, "F", _, 0]},
  Row[{Superscript[n + 1, 2 s + 1], Subscript[lsym, j]}]]

You also don't need Print to display your rule example:

angsym2[n1, s1, l1, j1] -> angsym2[n2, s2, l2, j2]

The Print was actually working, you just didn't understand what was happening. Also, you don't need the Return in your Module. The resulting value of a Module is simply the last expression in the Module.

I was being lazy about changing Piecewise to Switch. But I needed to understand modules better because I have to use Module functions made by others and I wanted to change them according to my needs. So, I am sticking to Module. Print is an odd command to use, but I didn't know about the use of Row like that. Plus I am using Return because in the other Module, I have many output statements and I need different statements at different times as written output.