Outlook to iPhone contact synchronisation
I hate to be the bearer of bad news but I have seen a lot of weird sync issues between iOS devices and Outlook/Exchange. As an FYI I am the admin for our 2013 MS Exchange server, so I see a fair amount of these.

Very little of what makes sense to do works reliably. I gather there is some kind of issue with Activesync on iOS devices and I have seen where some people claim it is an Apple bug and some, Microsoft's problem. The end result being it never gets fixed (so far...)

You can try the standard things with this, removing and then re-adding the account on the problematic phone, resetting network settings, doing a backup - reset - restore on that iOS device too; all are as likely to work as anything else.

The only permanent solution to the problem that I have found, and this may not be an option for some people, is to use Microsoft's free iOS Outlook email client rather than the email, contacts, calendar apps that come with iOS. I switched over a couple of years ago and completely stopped having sync and account issues with my Exchange-based (work email) email. And actually Outlook is a pretty good iOS email client.