Transfer data between "Custom Field" that appears in multiple places

Tenant azbestgaragedoor has a custom field "Permit Filed Date" that is set to appear on both the Project page and the Job page. The current issue is: whatever info is entered into this custom field on the Project page, that info does NOT transfer to the corresponding custom field on the Job page, and vice versa. Suggested improvement to Custom Fields feature: allow the ability to transfer info entered into the Custom Field in one location that it appears in to another location that it appears.