Usually this is because a user hasn't been assigned full Mercury SMS access, so they're not allowed to send SMS. The steps to fix this are:
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Go to Setup
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Go to Permission Sets
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Click Mercury SMS Full
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Click on Manage Assignment button
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Click on Add Assignment
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Select relevant users
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Click Next button at the bottom right
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Click on Assign button
If the user is a Salesforce Platform user, they won't be able to use the Mercury SMS Full License. In this case, they will need to be assigned the Mercury SMS None License in order to send SMS.