Patricia Zorrilla Bcn, sorry for the late reply.
I have checked and my user received email notifications just fine.
Are you 100% sure that the user who is not receiving emails notifications has "Immediately" under "My Preferences".
1. Since this happens to your own user as well, can you just change this user's email to something else ? Example if user used to have @gmail account, change his email to just another @gmail email.
Also try changing to totally another email (ex. @hotmail). This way we can check whether it is this particular email/email provider causing the issue.
2. Does this user get
site notifications? ( ex. that his has got 1 new unread PM notice in the
top right console of your site)