How to copy contact history from Leads to Customers

Alrighty, so I’m building a CRM. For my purposes, I have a Leads collection and a Clients collection. A lead becomes a client when we begin their first project.

At that time, I want to migrate all the info associated with the current lead and copy it over to a new client. All is working well, except for the contact history, which is a separate collection that I have created relationships with.

Each contact history has a “type”, “date”, “content” and two possible relationship fields: “Lead” and “Client”:

When I build the project and click the “Finish and Build” button, I have everything copied over from the Lead record to a new Client record, and I think I have it set up to transfer over the related contact histories, but it isn’t working:

The histories just don’t copy over. When I look at the available data for the screen, it doesn’t list Contact Histories.

What is the best way for me to get these over?

Thanks in advance for assistance.