After intercouse my husband has a sharp pain in his right testicle, what could this be?

Several things. It could be epididymis is ( infection or inflammation of the epididymis), it could be torsion of the testicle ( twisting on the vascular cord ) which is an emergency to untwist, kidney stones can cause testicular pain. If the pain is severe, he probably should be seen.
Some thoughts. There are a few things this could be, like infections, mechanical problems associated with the circulation of the testis, or tumors involving the testis or other structures in the scrotum. If this is a persistent problem, i would strongly recommend that your husband see his doctor or a urologist about this issue.