First: Office 2000 is not compatible with Windows 7 or 8.

Secondly, it's not entirely clear to me whether you're trying to run Office 2000 and Office 365 on the same computer - or at least have both installed - and whether both users are using the same computer. Furthermore, Office 2000 doesn't save to Office 365; it seems most likely you have both versions installed and you're both using the same PC, but the file associations for Word documents are tied to Office 365 on your wife's account.

Thirdly, you should never install an older version of Office onto a PC that already has a later version installed; doing so can create all manner of problems.

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Cheers,
Paul Edstein
[Fmr MS MVP - Word]