Present Perfect with another Present Perfect

I've got a problem. I don't exactly know how to use Present Perfect with another Present Perfect. In my there is sth like that: to describe two states that have exsted since a time in the past, for example: Since I've known him, he's always worn the same weater.
And now I have a sentence to correct:
I haven't seen Pter since he begins seeing his new girlfriend.

So I thought to myself - those two actions have begun in the same time, so I can use the structure Present Perfect with another Present Perfect. But book says that I was wrong. Why?

* In my book ...

I haven't seen Pter since he BEGAN seeing his new girlfriend

The tensed verb in the second part of this sentences is 'begin'. 'seeing' is not tensed, it is not used in any tense there.
You made the following mistake: the action that has continued to the present is 'seeing his new girlfriend' so this could be expressed with the Present Perfect (Cont.) Tense. The beginning, however, was one event - you can begin seeing somebody once, I hope that's clear. Thus, you can write:
since he began seeing
or
since he has been seeing...

Ok, I've got it. Thanks.