Hi partner,
We can use workflow to achieve it.
Go to Advanced Settings > Processes, new a workflow of Phone Call entity, uncheck Run this workflow in the background.

Select Sope to Organization, check Record is created and Record fields change, select Customer field.


Add a step "Check Condition", set the filter as follow.

Then add a step "Update Record", select Phone Call, set the update as follow.


Actavite the workflow.
In this way, when 1) a Phone Call is created and the Customer field contains data, 2) when a Phone Call is updated and the Customer field changes, the Form field will become Customer field value.