Looks like the issue is more related to Outlook for mobile. Please kindly understand that the Outlook tag here we mainly focus on general issues about Outlook desktop client. In order to better solve your problem, it's suggested to post your issue on this dedicated forum for Outlook for Mobile for more professional help. The following recommendations are for informational purposes only.
As far as I know, if you are transferring your Outlook account to a new device, it depends on your account type and settings. Here are some possible workarounds:
If you have an IMAP or Exchange account, you can simply add your email account to your new iPhone and sync emails from the server.
If you want to transfer all data from your old iPhone to your new iPhone, including emails, you can use iTunes or iCloud Backup and restore. More information, see: https://support.apple.com/en-us/HT204136.
(Note: Since the web site is not hosted by Microsoft, the link may change without notice. Microsoft does not guarantee the accuracy of this information.)
Hope this helps!
If the answer is helpful, please click "Accept Answer" and kindly upvote it. If you have extra questions about this answer, please click "Comment".
Note: Please follow the steps in our documentation to enable e-mail notifications if you want to receive the related email notification for this thread.