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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.
As far as I know, signatures between desktop and mobile devices do not support synchronization.
As a workaround, you can copy and paste your signature from previous emails to make sure it shows up the way you want. You can refer to this blog post to optimize your signature.
https://blog.gimm.io/how-to-optimize-your-email-signature-for-mobile-devices/.
(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.)
However, the signature line on the phone doesn't support HTML, so things like images or icons won't appear in the mobile signature.
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