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Jira's email handlers (and most of the apps you can get that are more clever than the built-in stuff) do not really care about the format of the email address. They do use the email address to try to match a user on their email address though.
So there's two points of failure to investigate, Jira and mailboxes.
On the Jira side, this is about how your handler or channel is configured, and whether you have users with matching email addresses. In "plain" Jira, there are a number of handlers you could use, and configure differently.
Let's imagine you've got Alice, Bob, and Charlie, all @Foo.bar. Alice can log into Jira, Bob has not used it yet, and Charlie is a customer.
I tend to use "create or comment" set to "create new user". If an email arrives from Alice, Jira creates an issue or comment with Alice's name as the reporter or author. If it's from Bob or Charlie, it creates a Jira account for them and names them as the reporter or author.
JSM is similar, but it will create Bob and Charlie as customers, not Jira users, if you have set it to do that.
Once created, all systems will look at the email address to determine the account.
But, you could turn off "create new user", in which case, Jira will ignore the email, because it doesn't know them. Could that be it here?
The other place to debug is the mailbox - does the Jira handler log show it reading and rejecting? If not, then does the email inbox still have all the incoming emails in it?
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