How to share reports between different public groups in salesforce?

Share a Report or Dashboard with a Group in Salesforce Classic
Enhanced folder sharing is the default option for all orgs created after the Summer ’13 Salesforce release. If you have orgs created before Summer ’13 and don’t want to reassign permissions for the legacy reports and dashboards, you can use legacy folder sharing in Salesforce Classic.

REQUIRED EDITIONS AND USER PERMISSIONS
Available in: Salesforce Classic (not available in all orgs)
Available in: Group, Professional, Enterprise, Performance, Unlimited, and Developer Editions
Available in: Legacy Folder Sharing

USER PERMISSIONS NEEDED
To share a report folder with public groups:
Run Reports AND Manage Dashboards OR Manage Reports in Public Folders
To share a dashboard folder with public groups:
Run Reports AND Manage Dashboards OR Manage Reports in Public Folders
On the Reports tab, hover over a report folder in the left pane, click  , and then select Share.
Select Public Groups.
Find the group you want, and click Share.To search, start typing a name.
Choose the sharing level you want to give this group.
NOTE Portal users can only have Viewer access to reports, and they can’t use dashboards.
Click Done, review your changes, and click Close.