So please clarify, when you say that the phone will not hang up do you mean it won't hang up a regular call, a messenger call or any call regular or Messenger?
Do you now own the device or does it still belong to the person mentioned? I ask because I would like to know if the device has been factory reset or setup with a new user or if everything is still the same from the previous owner?
Did the previous owner say when the issue started? I'm not sure what your contact level is like with the previous owner so I'll understand if this or other questions are difficult to answer. Usually I use this question to establish if whatever we're talking about at least worked at one time and stopped. My follow up question is do you remember if anything was happening around that time, new apps being installed, a SIM card change or any memorable event.
Have either of you manually cleared the app cache for FB? Intrusive apps like FB have a tendency to misbehave if they aren't managed correctly. Part of that management is regular restarts of the device. Restarting the device usually does things like clearing app caches, shutting down processes and restarting background services. If this isn't done regularly little bugs can form and start causing problems.
Have either of you uninstalled FB updates and then installed them again? The app likely cannot be uninstalled since FB is a preinstalled app on almost every device so removing the updates and allowing them to reinstall is the only way to get close to a "fresh" copy.
Is the hang up button dim in any way like it might not be accessible? So like with many options, when they are unavailable they may appear greyed out, like they are not selectable, in this case I would imagine the button will still appear red but maybe a hazy red like it is showing you the button but not allowing you to use the button, or does the button appear normally and simply doesn't work?
Does it matter who initiates the call? If you call out for instance, you are able to end outbound calls but not inbound calls or anything like that you've noticed?
Has any consideration been given to factory resetting the device? If it was FR in the past what was the result?
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