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As i know: Outlook mobile app does not automatically sync signatures created in the desktop application. And Outlook app for iOS and Android does not support HTML signatures by default. The mobile app uses plain text and probably converts the image in your signature to a plain text format.
I am afraid you need to add signatures on a mobile manually, and you may refer to the steps Eleni Constantinou mentioned below:
More Information: Is it possible to configure HTML signature on IOS outlook mobile app? - Microsoft Community
Please kindly understand that the Outlook tag here we mainly focus on general issues about Outlook desktop client. If you have any difficulties in the process of adding, it's suggested to post your issue on this dedicated forum for Outlook for Mobile for more professional help.
Hope it helps!
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