You need to have the correct MMS Settings.
Use this site to find your country and carrier then use the values they provide:
World Wide Mobile Phone Settings Or check the help pages at your Carrier's website.
WP 8.1: Settings > cellular + SIM > SIM settings > toggle "Manual Internet APN" to ON > tap "edit MMS APN" then input the values into the fields and select "save"
W10M: Settings > Network & Wireless > Cellular & SIM > SIM settings > Add an MMS APN > enter the values > make sure the "Apply this profile" box is checked > tap Save.
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