The Gemara in Beitza [quoted in full in the previous post] teaches that Moshe's shining face was a reality of which he would eventually become aware. But the Gemara doesn't tell us how he would know! Would he look in the mirror? Not likely.
Would someone tell him? "Hey Rabbeinu Moshe - your face is simply GLOWING!!" Maybe. Maybe not. People were probably soooo in awe of him they wouldn't feel comfortable telling him. So how would he know?
Maybe - whenever he met a Jew, that Jews face suddenly started to shine. Moshe realized that it MUST be from him.
משה רבינו העלה את ישראל איפה שהלך בכל מדרגותיו. איתא: הנותן מתנה לחבירו אין צריך להודיעו שנאמר ומשה לא ידע כי קרן עור פניו וכו' הא במילתא דעבידא לאגלויי, היינו שראה אחר כך בכל איש ישראל המשהו מקרן עור פניו.
(רבי אברהם מרדכי אלתר, אמרי אמת ויקהל תרצ"א)
I know a fellow who is very funny. When people see him, they start to smile before he even opens his mouth. Similarly, Moshe was so holy, he radiated his holiness to others.
