Check the user account's application access. It is possible that you activated the account, however if that user does not have application access to Jira Core or Jira software, the user won't actually be able to access those specific parts to the site. For example if he's expecting to see/create a board, he will probably need to be a member of the group that is granted application access to Jira Software. By default this group is called jira-software-users but it is possible that you could have a custom group that grants access to this.
Even if he then has application access, the next thing to check would be his project permissions. It's possible these have changed since he was active, or the group memberships might have been changed to his user account. Managing groups explains in some more details how to change this.
Another tool I like to use to troubleshoot problems like this is the User Switcher plugin for Jira. If you are an admin, you can use this utility to switch your browser session in Jira to use this person's account. You don't have to know their password to test this out and it can help to understand what the other user might be seeing in some cases.
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