Is "grab" an informal way of saying "learn"?

Solution 1:

Personally, I've never heard of "grab" as in learn, but "grab" as in "get" or collect is informal, yes. This is a definition from Wiktionary of "grab", and one of its usages, the one that seems to apply to your context, has been dubbed informal:

(informal) to quickly collect or retrieve

Grab, is an informal word, and presumably not advised to be used in your situation.
If that person is a kind of respectful, dignified person, than just simply writing "I"d like to invite you to somewhere where you will be able to acquire a lot of cultural and historical artifacts" would be better.

Or, if the object was not an artifact, but learning, then, perhaps try:

I would like to invite you to a place where we would be able to increase our cultural and historical knowledge

Solution 2:

I'd like to invite you to Somewhere where you will be able to grab a lot of cultural and historical artifacts.

This sounds like you are inviting him to a place where he can steal things found at archaeological digs.

Grab does not mean the the same thing as learn.

You may have confused grab with grasp. Grasp is equivalent to get in that they are both synonyms for understand. But understand and learn are not the same thing.