Hi Laura,
Move the report schedules across different reports is not currently possible.
However, looking at the way you actually deploy the reports, here is what would be a good process, provided you are using and deploying Jaspersoft Studio Reports:
1. Create and test the report in Jaspersoft Studio
2. Save the output as jrxml file on your local machine
3. Now connect to Jaspersoft Console as superuser account
4. Navigate to the Reports, find the report you want to replace, right-click - Edit
5. In section Set Up, Upload a Local File - Browse and upload the new jrxml file
6. Click Submit
This will replace the report with the new version, and should keep the report name and schedules as they were before. This will also help you with not having too many instances of the same report on the server, which can confuse the users.
Please note though that we recommend you do testing on lower environments first before promoting the report query to Production.
Also we recommend you keep all the jrxml files backup on a shared server so in case you need a replacement or a rollback, this is easily possible and they're accessible by the team.
P.S. Please note that the OOTB reports should not be replaced as any changes will be overwritten during upgrades or patches installation. If you need to modify an OOTB report, you have to use a copy of it, the steps are described here:
https://docops.ca.com/ca-ppm/14-3/reporting/jaspersoft-studio-report-development/create-and-publish-jaspersoft-studio-reports
Section Create a Report with Sub Reports
It shows how to copy a report with sub reports and post to another environment, same steps can be used for copy of OOTB reports too.
Hope this helps -Nika