There really isn’t any way to migrate these fields with just the ACF plugin. It depends on how the other plugin saves data and if that data matches up with how ACF saves data. ACF also requires a field key reference in the database for fields that are created using ACF. ACF will not access the field values created by another plugin.
Since I am not familiar with the other plugin I cannot advise you on how this could be coded.
A non code method of doing this would be to user WP All Export/Import Pro to export the data and then import using the ACF add on.
