You will only be able to view and select letter groups if you have the view permission for the group in question.
This can be added either to one of your roles or can be set up on the group's settings page.
Add the permission to one of your roles
Go to Setup, then Roles & Permissions.
Click one of the roles that is assigned to you and that will need to see this letter group.
Click Role Permissions, then Edit Permissions.
Search for the name of the letter group and click the eye icon so it's set to green.
Click Save.
⚠️ Important: Please keep in mind that once you do this all employees with this role will be able to view this letter group.
Change the settings on the letter group
Another way of doing this would be by changing the settings on the letter group itself. However, if you don't have permission to view it, you will also not see it in the Content menu.
This option works if you already have access to the letter group and would like to give someone else access as well.
Click Setup, then Content.
Click Mail Merge, then select the letter group.
Click Edit Group, then click the View Permission tab.
Select the roles that need to see this letter group.
Click Save.