You may want to save a shared report as favorite. So you will be the report owner and can share the report to other people in your team.
Please follow the below steps to save a shared report as a favorite:
1. On the left navigation pane, click Reports.
2. Click Shared With Me tab.
3. Click on the report name that you wish to save as a favorite. This will open up the report on the screen.
4. On the report, click Show Options on the right top.
5. On the Options tab, click Run button.
6. After the report is pulled out, click Star icon on the right side.
7. On Favorite Report dialog box, enter the report name and click Save button.
The report is now showed under My Favorites tab.