Signed into old Apple ID no longer in use

I just got a new phone but I am waiting to set it up because my current phone has problems with Apple ID so I wanted to try to make sure nothing will be lost in the process. Right now I am signed into my brother's old apple ID that he no longer uses. I have tried yahoo and apple support to try to recover the password and neither have worked. My appstore app is also broken (when I open the app it closes right away) but when I try to update storage it asks me to sign into the apple ID which I can't get into. I want to have everything under my name and my own apple ID that I have created but it won't let me do that until I sign out of my brother's apple ID by entering the password (that I don't have).

[Re-Titled by Moderator]