How do I switch from Windows Live login/password to local without Live password, but with Administrator access?

A friend recently passed away, and his wife asked me to gain access to his Windows laptop for which she doesn't know the password.

When I try to guess the password, I get this error message:

You can't sign into your device right now. Go to account.live.com to fix the problem, or try the last password you used on this device.

I can't change the password on account.live.com, because the email address associated with the account no longer exists.

I took the computer offline and tried again, and I get this error message:

Your device is offline. Please sign in with the last password used on this device.

I tried this method, which got me access to cmd.exe and allowed me to change the passwords for all of the local users. But that doesn't allow me to log in; it still tells me I need "the last password used on this device".

So it seems that changing the local password isn't good enough, and that I actually need to know the last password used. Or at least be able to change that.

Does anybody know how I can hack this computer so that I can log in?

Thanks.

Update: I am now able to log in as Administrator, thanks to the help below. I still cannot log into the target account (same error message). I also cannot figure out how to switch it from Live to local login whilst logged in as Administrator.

Update: I changed the title to reflect my current situation: I have Administrator access to the laptop, and can change the target account's password. But I can't figure out how to change the target account from Live to local.