Can Blitzcrank move enemies from one Battlefield to another Battlefield?

Ruling: Yes, Blitzcrank can move enemies from Battlefield to Battlefield. There are no restrictions on the source of his target.

Nuances:

• Only standard moves have restrictions on moving units between Battlefields
• All other moves (like Blitzcrank's ability) just do what they say without additional restrictions
• Charm can also move units from Battlefield to Battlefield despite not providing explicit detail