First of all, let me just commend you on how clearly you showed the issue about which you are posting. I do not play career mode, but I may be able to assist.
May I ask: do other changes you make take effect? For example, if you change the shirt to tucked in or something along those lines are you able to save them? If not, there must be a step you are overlooking... perhaps needing to click save again and then going back into the edit player menu in order to see the changes.
Is it possible that you are unable to change to a number that is already in use by another player on the squad?
Finally, a simple workaround would be to edit the squad file using RDBM and just change it that way.
Let me know if I can assist further (if I have assisted at all lol)
First of all, thank you very much for having answered me and for being able to contribute your knowledge.
I uploaded another video changing the t-shirt, the shoes, everything changes except the number! I also tried to modify it via Cheat Table but it only takes effect for 1 match, I have to redo the manipulation each time.