My experience as a "Jr."
I've been through this lots of times, as I'm a "Jr." and also often use a middle initial. My passport has my full middle name, and air reservations will sometimes show the "Jr." and sometimes not. They sometimes put the "Jr." in a different field from the last name, and sometimes add it as 2 letters at the end of my last name, such as "SMITHJR".
I've never had a problem checking in or clearing security for an international flight, and I fly international a lot. Here are the minor glitches your partner will run into, just so you know what to expect and not to worry:
Most airlines have you check in at a kiosk, where you swipe the passport. The passport swipe will fail 100% of the time, and it will just say to check in with an agent. The computer gets wigged out by the suffix issue, but an agent always checks me in just fine, once the agent realizes it's just a suffix issue or middle-initial issue. This has been fine checking in not only in the US, but also in Italy, France, UK, Netherlands, India, Vietnam and Cambodia. So basically not a problem anywhere.
Therefore, don't waste your time trying to reissue the ticket. That's totally unnecessary.
The only problem I've run into is with TSA PreCheck. When I was in the PreCheck program by invitation, that program is based on your name and frequent flyer credentials. An EXACT name match is therefore necessary. After spending countless hours on the phone with airlines trying to massage my name to match the TSA records (Delta has been particularly patient and cooperative about this, time after time), I finally threw up my hands and got Global Entry. Now that I've got a Known Traveler Number, the name match is no longer necessary. Problem solved. If PreCheck is important to your partner and he's had these issues, he should consider Global Entry.
If you or he have any more questions, feel free to PM me.