delete admin

While the laptop may not have been used much it still is a good idea to perform a clean install of macOS. Here is an Apple article on how to prepare a Mac for sale or transfer of ownership:

What to do before you sell, give away, or trade in your Mac - Apple Support

However, if you are able to log into the Mac you can create a new admin user account.

Set up users, guests, and groups on Mac - Apple Support

Once created, logout the original user account and log into the new admin user account where you can then delete your mother-in-law's old user account. You may also need to change the network name using the instructions in this Apple article:

Change your computer’s name or local hostname on Mac - Apple Support

deleteadmin Said:

"delete admin: I was given a 2015 MacBook Air by my mother in-law, She never used it. I have cleared it out and reset it. I have gone into her Apple ID and removed the device from the form. When I go to start up the MBA her name still shows up, please advise"

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A Quick Question:

Are you unable to delete her account, through use of a new user account?