You'll get that pretty much automatically, as the recipe coming from the back gradually rebuilds a copy of the universal constructor's memory storage unit, and then repopulates it from a data stream coming from the parent copy, which self-destructs as usual once the data is sent.
Seems like it's perfectly workable, and it's a simpler design in some ways than the Speed Demonoid and Speed Orthogonoid, because the crabstretcher or blinker puffer never have to be destroyed and rebuilt. On the other hand, the new mechanism will have to be some kind of loopship (right?) unless it uses stable memory storage like the design that we managed to avoid in the RCT. We have Goldtiger997's examples of fast spaceships that build memory loops big enough to hold their own construction recipes, so we know roughly how big something like this would be.