You've probably noticed that it isn’t possible to sync Lead Source or Contact Owner through the Field Mapping like any other field. Instead you will have to map this field in the connection Rules. See below on how to do so with contact owners:
In this image you can already see one reason why PieSync does not display these fields in the field mapping. The way ownership works can differ vastly per app — not to mention that not every app may have the same owners. In this case Copper distinguishes on name, while HubSpot on email address.
As such, we've found that the best way to enable you to sync your owners, is through the filters and action. The downside here is that you will have to create a separate rule for each owner that you want to keep in sync.
When looking at the way the Source fields work, we find a similar situation. If you are not able to map the source field through the Field Mappings, you can try to do so through the Rules:
The Source field often does exist in the Field Mapping, but connecting it to another source field probably doesn't work. That's because both or one of these fields is a dropdown field. PieSync is not able to see which values should be mapped to one another and will require you to do so on its behalf.