With 3.6 of Create on Transition for Jira, there are now two ways to copy a custom field value to a different custom field. The new way provides the ability to do this for more fields than before.
For this example lets say you want to copy the value of source_cf to target_cf for the newly created issue of subtask.
This is the easiest approach provided you have enough Set custom field slots to use for your needs.
These fields normally just list custom fields you wish to copy to the new issue. This is the best way to copy fields exactly to the newly created issue. As many fields as you like can be copied this way. However, it can also map the value from one field to a different field. This is useful when you have a significant number of fields to copy.
Both Set custom field and the mapping support provided in the Copy case map be impacted by custom field type specific peculiarities since both techniques use string values for setting the field. See Custom Field Types for a list of known supported types.