The user profile permission - Edit Tasks - can restrict access to the Salesforce for Outlook add email envelope icon
|Knowledge Article Number||000239649|
If you have the Add Email option enabled in your Outlook Configuration, and you're not seeing the Add Email envelop icon, we'll cover how to solve that problem.
|Resolution||This issue is typically profile permission related. Check to see if the 'Edit Tasks' perm is disabled on the custom profile. If it is, you won't have access to create Tasks.
If this article didn't solve your problem, you'll want to read our help article Add Email envelope icon is missing from the Salesforce for Outlook in the Side Panel.