Herpesvirus is spread by direct contact. Theoretically, if he touched
his eye and then yours, or blotted the discharge on a towel or tissue
which you then applied to your eye, or perhaps you handled that towel
and then touched your eye.............

So, not very likely.  A more important question is where did he get it,
because is certainly possible that the virus exists somewhere on his
body that he touched and then touched his eye.

-LB