Thank you for your message and I am sorry to hear that you are experiencing some problems. I would like to try and help you but to do that I would like to request a little bit more context.
I understand this problem exists in Office 2016 in all applications. Does that mean that for example web-users do not have this issue, is it limited to user of the desktop clients?
How and when did you find out this problem exists? Can you give some information on when it started? Did you maybe updrage the Office 365 applications on the users machines?
Is there a certain destinction that can be made between the users that have this problem and the users that do not have this issue? Are they all on the same OS and versions?
Finally I would like to know where the spinner gets stuck, is this after clicking to send the SMS, or after entering the code?
I hope this information will give me some context as well as more ability to test if I can reproduce the problem.
Thanks you, regards,