PSOFT GM/PC Organization needs to be a recipient and a sponsor?

Please forgive my ignorance, trying to learn best practice and how best to apply knowledge into GM/PC. I am more of a HR guy... How can I make the organization I am working with both a sponsor and a recipient? For grants. They have an exception in their business process that gives a grant to an agency but it is given by the organization not as a pass through entity.

What is the best business process or how would you best make this happen?

where state is a sponsor (giving) and not the recipient from the fed... Would it be considered a subrecipient and the project funds are generated from the recipient? Please help <3