I create customer request and send it to the email, which set in the Salesforce and the Jira Service Desk as the custom email address.
Salesforce catches this mail first and marks it as "read". Jira doesn't work with messages in status "read" until I set it as "unread", after that it creates issues and send the notification.
How do I set Jira for notifications?
This is not something that Jira Service Desk can do natively. It is designed with the intention that Jira Service Desk will be the only application using that specific mailbox. More details about this in Receiving requests by email.
It might be possible to achieve this in Jira Cloud with the use of a 3rd party plugin. Off the top of my head, I would try to see if perhaps something like the Enterprise Mail Handler for Jira might be able to accommodate this. I'm not sure if it can do this, but I can't think of any way that you could do this with just Jira alone. I also tried to see if perhaps there was some Gmail labs feature that might be able to accommodate this, but I haven't found anything yet that would do this. The possibility of duplicating issues within one application or the other seems like it would be rather high and difficult problem to overcome here.
For JSM June Challenge #2, share how your non-technical teams like HR, legal, marketing, finance, and beyond started using Jira Service Management! Tell us: Did they ask to start using it or...
Connect with like-minded Atlassian users at free events near you!Find an event
Connect with like-minded Atlassian users at free events near you!
Unfortunately there are no Community Events near you at the moment.Host an event
You're one step closer to meeting fellow Atlassian users at your local event. Learn more about Community Events