For JIRA administrators

The system admins can change the ownership of a dashboard/filter directly from the dashboard/filter. The option 'Change owner' is conveniently located on the dashboard/filter page.

For dashboards, the option is located both in the 'Dashboard information' dialog and the Tools menu

For filters, the option is located in the 'Details' dialog

If the JIRA administrator changes the owner of a dashboard/filter:

If the new owner is among the list of 'Share ownership' of the dashboard/filters, the list of co-owners remains unaffected. It is as if the new owner took ownership via the Take Ownership button.
The list is reset if the new owner is not among the dashboard/filter's co-owners. The new owner can share ownership with anyone as required.

As an administrator, you can transfer a dashboard or filter to yourself, make changes to the dashboard’s gadgets or the filter’s JQL (without editing the shares), and then give the dashboard or filter back without erasing the old co-owners.

This works because if you change the owner of a filter or dashboard with shared ownership and the new owner is not among the old co-owners, the old list of co-owners is disabled but not erased immediately. The list is remembered until the new owner makes any changes on the filter/dashboard sharing page. If the ownership is transferred back to one of the old co-owners without making such changes, the old co-owners list will be reinstated.