"By way of information"
What does it mean? Is it correct for a formal letter?
It's a way of saying take note, or you should know or you should be aware of the following information.
It's used in all kinds of formal and semi-formal communications but would sound odd between friends.
So an agency might well say:
By way of information, the airline offices will be closed next Friday but your reservation will still be accessible online.
Informally, you might tell a friend.
By the way, the airline offices. etc.....
It's fine for a formal letter but might sound a bit presumptuous from an applicant to a company or university.