Copying data between Cosmos DB containers in different tenants can be support, but bit complex.
Step 1: Set Up Access
Source Tenant: Ensure you have read access to the source Cosmos DB container.
Destination Tenant: Ensure you have write access to the destination Cosmos DB container.
Step 2: Export Data from Source Container.
Step 3: Import Data to Destination Container.
Step 4: Verify Data Transfer
Alternative: Using Azure Data Factory
Create a Data Factory: In the Azure portal, create a new Data Factory.
Create Linked Services: Set up linked services for both the source and destination Cosmos DB accounts.
Create a Pipeline: Create a pipeline with a copy activity to transfer data from the source to the destination container.
Please refer the documentation link, it might be helpful to you
copying data from a cosoms container in one tenant to cosmos contianer in another tenant - Search
Hope this helps. Do let us know if you any further queries.