From nraila.org :
NON-RESIDENTS
A non-resident is permitted to possess a firearm without a FOID if it is unloaded and enclosed in a case, or if the nonresident is:
• Hunting and has a non-resident hunting license, while in an area where hunting is permitted.
• On a target range recognized by the Department of State Police.
• At a gun show recognized by the Department of State Police.
• Currently licensed or registered to possess a firearm in his state of residence.
Any resident of Iowa, Missouri, Indiana, Wisconsin or Kentucky, or a non-resident with a valid non-resident hunting license, who is 18 years of age or older and who is not prohibited by the laws of Illinois, the state of his domicile, or the United States from obtaining, possessing or using a firearm, may purchase or obtain a rifle, shotgun or ammunition for a rifle or shotgun in Illinois. A non-resident who qualifies to possess a firearm under one of the above-listed exceptions may also purchase ammunition.
Look at what's in bold. I think you're G2G with your sale...