The original: "... he's gone to one of his student's birthday party."
My suggestion: ...he has gone to the birthday party of one of his students.
Unless there were several students having birthday parties that day, in which case it might be: ...he has gone to one of his students' birthday parties, which could be disambiguated* as ...he has gone to one of the birthday parties of... no, no, that's going to be too awkward, let's try ...he has gone to one of the parties that... no that's still going to be ambiguous, ...he has gone to one of the birthday parties that... no that still won't get it, how about ...he's not here.
*I originally had disambguified† in here but Ænigma suggested disambiguate so I went with that.
†Yeah, I had to misspell disambiguified to get disambiguate; it wanted to disappear disambiguified
