"It is fun to write letters" vs. "It is fun writing letters"

Grammatically, "It is fun to write English letters." is correct. But is the following also grammatically correct?

It is fun writing English letters.

Solution 1:

Both Gerund and Infinitive Subject Complements can be Extraposed -- inserting a dummy It -- with the predicate adjective (be) fun.

• (For Indef) To write English letters is fun. ~ It is fun to write English letters.
• (Indef('s)) Writing English letters is fun. ~ It is fun writing English letters.

This is not necessarily true with other predicates, which all have unique patterns, as the second link should make clear.