Interstate sales require use of an FFL for transfer.
For long guns, the FFL can be from either the origin or destination state.
For handguns, the FFL must be in the destination state, per Federal law.
Plus you'd have to comply with whatever laws Illinois has in place.
Note: Internet advice is worth what you paid for it; I am not an attorney. It is never a bad idea to address this type of question to an attorney, or to your local BATFE office. That said, the answer I gave you is the one that I've been taught.