Some months ago when I was at work, a checkroom, an old lady

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Some months ago when I was at work, a checkroom, an old lady came up to me to hand me her coat.
I always try to be polite and look people in the eyes, cause you know, the tips are better if you look people in the eyes like you deserve a tip.

Anyway, so this lady comes up to me and greets me.
I look up and for a fravtion of a second I thought I saw a friend of mine who is just 21 years old though.
At first I was clueless why this thought even crossed my mind seeing that old lady but as I looked at her longer I realized she had not only the same eyecolor as my friend, but also the same expression.
It was like she came from the future to say hi, but that's not what I want to allude.
It was like my friend looked at me through the eyes of this old lady.
On top of all of that, that lady looked at me like she knew me for several years already.
I get goosebumps just about thinking about this incident.
Needless to say she also gave me a generous tip.

I know it happens that some people look similiar to each other and that some eyes might have the same expression as others but this wasn't just a similiarity, it was, as I said, like my friend was looking at me through this old lady.

Is there a name for this phenomenon?
I can't imagine being the only one who experienced something like that.

Did you guys experienced something similiar? Do you know where I can find more about this topic, if it's even a topic that is widely known.