Transfer Zephyr content via Jira connection

Hello,

I am trying to connect Jira including Zephyr Squad to another system. The connection is working fine and I can transfer the Jira issues "Test" (created in Zephyr Squad) from one system to the other. However, all Zephyr-related contents such as test steps, data, results, attachments, and reports cannot be chosen for transfer. Is there a solution to transfer this kind of content via the same connection? Traceability to the Jira issue must be maintained. Or would I need another connection in this case? Thanks in advance.