We did write how a blog on how to check Einstein Analytics License Assignment, this blog will share about checking Inbox license in Salesforce Classic and Lightning.
Inbox License Assignment are pretty similar to Einstein Analytics License Assignment, you can see how many Inbox total licenses you have, how many licenses used and remaining licenses in Company Information under Permission Sets Licenses in the setup menu.
Next question, I would like to see who has this licenses assigned? If you are in Lightning, this is pretty simple, search for Inbox in the setup menu and you will see Users and Licenses.
But, how about if I am still in Classic? short answer, flip to Lightning :) anyway, you can run SOQL to get the user if you are still in Classic, here you go
SELECT Name, Id FROM User WHERE Id IN
(SELECT AssigneeId FROM PermissionSetLicenseAssign WHERE PermissionSetLicense.MasterLabel ='Inbox') AND IsActive=true
ORDER BY Name
Next, if I manually open the user detail, how I can see if the license has been assigned? Is it under Permission Set Assignments or Permission Set License Assignments related list? This is exactly the same with Einstein Analytics licenses assignment, once you add the Permission Set, the Permission Set License will be auto added, but not the other way round.
From above screenshot, once you add "Inbox With Einstein Activity Capture" permission set, Inbox license will be auto-granted.