You can restrict your users' access to each channel and shared email account in Inbox.
If a user doesn't have access to a specific shared inbox, you will not be able to assign a conversation in that inbox to that user. You will need to add the user to the inbox first.
Adding or Removing a User from an Inbox
Click into your Inbox and click the gear icon on the top right to navigate to the Inbox settings.
In the Inbox settings, select the shared email account you would like to give a user access to.
Click the gear icon on the righthand side of that email account. That will pull up the settings for that particular email account.
In the settings window that appears, click the "Users" section.
In the dropdown that appears, you'll see all the users that currently have access to this email account. Search for the user you would like to add and select them.
Note that if you are trying to remove a user from a shared email that is set as the default for a pipeline or process that that user has access to, you will need to do one of two things:
Remove that user from that pipeline or process so they no longer have access
Make the email account no longer the default for the pipeline or process (in the next drop down menu under the users menu). Note that you will only want to do this if you do not want this email to be the default sending email for that pipeline or process.
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