I plan on going to Lipetsk to stay with a Russian friend for a few months to study Russian and I won't be working. I plan on getting a multiple entry business visa and a letter of invitation through a visa agency.

Assuming that the letter of invitation will be from a Moscow business - Will this be a problem when I go to Lipetsk and register there? Or is the letter of invitation only used to get the visa and not important when I register?