If the email account is now in your Family and Friends section I would say that you have successfully transferred it to your BT Broadband account and it has now become one of your eleven permitted email accounts.
Apologies for speaking as though she is still alive but it makes it easier to explain.
As per the link I posted you are advised to "gift" it to the person whose email it "was" (your mother) so that they can keep control of the email account and be responsible for its security and to be able change the password because during the process you would now know what the password is ( I know you already knew it but you might not have).
It would appear that this has already been done because the email account is in your Friends and Family and missing from her MyBT email section.
Because your mother already has a BTID which was linked to another BT Broadband account which is now going to be closed, it would require her to accept the email account and set up a new BTID as per the "gifting" process. It would still remain in your BT Broadband account but the security etc would now be her responsibility.
You would then only be able to access it through her new BTID and new MyBT.
As the email account is no longer in her "old" MyBT I suspect it is waiting to be accepted by her with her new BTID.
The acceptance email should be in her Inbox although if it is not there check in the Spam folder.
The username (presumably her email address) and her password would remain the same until she (you) changes the password via her new MyBT.
The link I posted does explain the above if you follow all the sub links.
