Ask the seller to connect its crate mark and handover record to the agent's booking reference, then ask the agent what physical receipt it can confirm against that link. You need the handover matched, not another description of what shipped is supposed to mean.
Keep that distinction in your next message. Ask who at the seller can supply the actual handover evidence and who at the agent can check it. A recognised booking is progress on the reference problem, not confirmation of custody.
Then leave the installation date unconfirmed for whoever is planning the sorting setup. You can pass on the matched booking without turning it into an arrival promise nobody has actually made.