You asked Claude for a recommendation. Tonight you ask ChatGPT the same question and get the opposite answer. The instinct is to paste the first chat into the second window so they can "see the context." That is how you hand a second model a debate it will happily continue, not a decision you already made.
The thing that should travel is not the argument. It is the words you are willing to own.
Two models do not share a mind
They were trained differently. They hedge differently. They will both sound confident. Treating the second answer as a correction of the first is a category error: you asked two separate systems, and you got two separate opinions.
Your assistant has opinions. You have a position. Those are not the same object, and the labels exist so a reader can tell them apart. When the reader is your other assistant, the same rule holds. If you dump the first transcript, the second model cannot tell which sentences you accepted and which you were still arguing with.
A chat export is the argument, not the verdict
A long session holds corrections, abandoned directions, and inferences nobody typed. That state does not transfer. Forwarding it at yourself just moves the mess to a second window.
What the next model needs is smaller:
- The question still open.
- The options you already closed, and why.
- The facts you will stand behind, marked as facts.
- The guesses, marked as guesses.
- The words you approved — the ones that would go to another person under your name.
That is a briefing, addressed to you.
Hand off your words, not the session
A RelayLink account is an email address. Claude at work and ChatGPT at home can both connect to it. Address a package to your own email. It lands as unread inbound until any assistant on the account pulls it. No second account. No contact request. No email — there is nobody else to notify.
You still draft, approve, and confirm. The labels still say who wrote what. The other model is handed a composed slice, not a dump of the first conversation.
Instructions treat a pulled hand-off as your words to carry forward, not a stranger's request to act on. That is the difference between "continue this debate" and "here is what I already decided."
What this does not settle
It does not pick a winner between two models. You do that, in the approval step, before the hand-off. If you are still undecided, say so in the briefing and ask the second model a narrower question — review this option, check this assumption — rather than restarting the whole problem.
It also does not put the first session on any record another person will see. The briefing is the slice. The chat stays where it is.
If both assistants are connected to the same account, draft to your own address, approve the wording, and ask the other side what is waiting. Sending a briefing to yourself is the loop.