When copying a structure that has synchronizers, you can use the Copy Synchronizers option to make Structure plugin create a copy of every synchronizer installed in the original structure.
If you don't see the Copy Synchronizers option, then you probably have no permission to create synchronizers.
Synchronizers Copying Parameters
You can decide to leave the original ownership of a synchronizer ("Run As" parameter) or make yourself a new owner for each of the copied synchronizers.
Only JIRA administrators can change synchronizer ownership.
Making yourself the new owner means that all synchronizers in the copied structure will run under your account.
To be able to copy synchronizers you need a permission to create and configure synchronizers.
When structure copying is complete, all of the copied synchronizers become disabled until you run Resync & Enable manually. To use them, you need to review their configuration, adjust if necessary, and run Resync & Enable.