Processes in Microsoft 365 for setting up Office apps, redeeming product keys, and activating licenses.
It is not possible to add the @Live.com Email as an alias to your @Outlook.com Microsoft account, because those are two separate Microsoft accounts, there is also no native method available to move a Microsoft 365 subscription from one Microsoft account to another account.
The only option would be to cancel the Microsoft 365 subscription to get a pro-rata refund, then take out a new Microsoft 365 subscription on the other account.
You can check your eligibility to a refund using the steps on this link.