familiarity

Alla: - Irina! Come on I'll introduce you to my school friend Natalie.
- Natalia Hello - this is my colleague Irina.
- Irina - this is my school friend Natalia.
Natalia: - Hello! Nice to meet you.
Irina: - Let us know and I am happy to meet you too.

I am not sure why you wrote "Let us know."  Does it refer to another part of the story?

Also, school friend is OK, but I would probably say "friend from school."