If the gun is legal (e.g. not an unregistered full-auto), then the process would follow along the following lines:
Your father would need to get a FOID card. Possession of a firearm in Illinois without a FOID card (provided he is eligible for a FOID card) is a Class A misdemeanor. If he's not eligible (wife beater, gang member, felon, etc), then it's a Class 4 Felony.
FOID in hand, he then needs to have the gun sent to an FFL in your home state. As Illinois and Montana do not have mutual provisions allowing the transfer of long guns between them by unlicensed persons, this is the only legal way for it to be sent.
Illinois law requires that a record of private transfers be kept for 10 years following the date of the transfer. Meaning that your dad is legally required to keep a bill of sale/receipt of transfer/some kind of paperwork with details of the sale/transfer.
You will need to go to the FFL in your home state who will then conduct a background check in accordance with Montana (or wherever you actually live) and federal laws.
Note: THIS IS FOR A LEGAL FIREARM. If your dad sends off a bring back PPSH-41 both of you could see some major pound your ass federal prison time. This is not a joke. You need to make sure that it's not a short-barreled rifle or a machinegun. Or anything else that is not legal without federal registration.
Again, this is a basic guide for a legal gun given the circumstances you've provided. Your best option would be to contact an attorney in your respective states to clarify anything that could be a problem with the process. Do NOT just haul the gun back across state lines after an illegal purchase.