Welcome back to the Wefugees Community and thank you for your question.
I don't think this will cause any problems in the future, since he also applied for a new appointment before the residence permit expired, right? In these days immigration offices most likely need more time for offering appointments and dealing with the applications as they are also struggling with the Corona regulations etc.
In Berlin, for instance, the immigration office/Ausländerbehörde introduced an online-registration tool for people whose residence permit/toleration (Duldung) is expiring. The print/PDF of this form serves as temporary extension until the immigration office invited for a renewal appointment and can also be shown to the Jobcenter etc.
I hope this helps and please feel free to get back to us with any further questions.
All the best,