Corollary: Transport of the complete recorded instrument

If the clock is read at the sender and its record is causally forwarded with the surviving payload, the receiver obtains

where $\mathcal{V}$ is the exact relocation identity. Any record-controlled operation at the receiver is performed only after both required inputs arrive. This is the same complete instrument with relocated output.

Proof. Apply Theorem thm:transport with the classical record included in the reference. Forward that jointly classical record explicitly, then apply the same conditional maps at the receiver. Equality holds blockwise, including references.