Be aware that there was also an 87th Infantry Regiment, which was part of the 10th Mountain Division. So first you must confirm that he was in the 87th Infantry Division.
One of the best places to look for this information in on the military discharge. Please note, however, that even if your grandfather did serve in the 87th, this may not be detailed on his discharge, as he may have served in other outfits as well.
Submit a Standard Form 180 to the National Personnel requesting your grandfather’s service records. Unfortunately, there was a fire in 1973 which destroyed about 80% of the Army’s records for the time period between 1912 and 1960. You may, however, be in that lucky 20%, so it’s worth a try.
This information can often be found on medical records. Request a copy of your grandfather’s Service Medical Records (SMR) from your Regional Veteran’s Administration office.