Microsoft mail servers filter they spam very agressively (specially
emails written from open source clients). The problem is that those
messages are completely deleted by the receiving server, and the
sending server receives no acknowledgment that the message was
discarded.
I have had that problem writing to people in organizations that have
Microsfot Exchange server and they didn't receive my emails.
Free accounts in Gmail, Yahoo Mail have spam filters that are
sometimes too agressive. Messages goes to the spam folder, but they
still kept in the spam folder. Microsoft servers just delete
completely those messages.
Gmail, yahoo, gmx are very bad for privacy, but M$ goes to another
level. They also intend to destroy the usability of the email
protocol, and the use of open source clients/servers.
I would try to send a test message from gmail webmail. To be sure
compose the message via the webmail (not in an external client).
Microsoft doesn't dare to bully gmail users. Google is very powerful
and almost everybody nowadays uses gmail.
I guess she wants to use some extra features of
outlook.com
(calendaring or something related to Office 365). That's how
Microsoft infested the corporate market, through the 'extra features'.
Nowadays most organizations use Microsoft Exchange server and
corporate email has become totally unreliable.