the OP is asking about a 1 year trial version of 365 on her daughter's new computer which she is trying to activate on her computer.
There is no "1 yr trial". There are only 30 day trials, and in very specific situations a 6 month extension of the 30 day trial only for Pro Plus.
The "came free" Office 365 is a "real" subscription. From other people who asked about this "free Office" I got the impression that is was a normal Office 365 Personal subscription. So one question that has come up in this discussion is whether it really
is a "normal" / "off the shelf" Office 365 Personal subscription, or some new weird and wonderful critter. Say "Office 365 Personal OEM", that has special license terms, like who can activate it (computer "owner" only?). I repeat, nothing I've heard or read
(in Office 365 MS License Terms) suggests that this free license is anything other than a "normal" 365 Personal subscription as defined in the MS License Terms.
So, assuming it is a "normal" 365 subscription, when it is properly activated on an email account that already has 365 Home or Personal on it, the existing expiry date is extended by one year (adding 1 year to the original expiry date). If it was 365 Home,
it is "upgraded" to 365 Personal (with the extended expiry date). If needed, that new 365 Personal can then be converted back to 365 Home with a second extension by activating a 365 Home Product Key on the account (the original expiry date + 2 years).
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The OP said there was no sign of 365 Personal on their (or their daughter's) account(s), so apparently there was a problem during activation of the "free" subscription. We still have no idea what went wrong.