In Blade Runner 2049, what exactly happened with the horse?

Question

In Blade Runner 2049, Dr. Stelline implants one of her own memories into K's. This memory concerns a wooden horse on which is written an important date, and K is able to use this memory to locate it at an orphanage decades later. He is able to trace it back to Las Vegas thanks to a telltale radiation signature. I have two questions regarding this horse:

a) My understanding is that Deckard left for Vegas before Stelline was born. If he did, how did she end up with the horse which had apparently been made, or at least spent time in, Vegas?

b) Why exactly did Stelline implant the memory of the horse? Presumably this was done deliberately, as it would potentially allow a replicant to locate Deckard. Did she simply hope someone would be able to bring him to her? Wouldn't that risk (indeed, perhaps probably guarantee) exposing her identity to Wallace? Also, K only becomes interested in finding the horse when he sees the same date at Sapper's farm, through an apparent coincidence. Was there more going on there?

Answer 1

This will be a tricky one, since it's still very early in the release of the movie and most of us don't have a hold of the scripts. Additionally, this entire plot point is shrouded in mystery. Luckily, I watched it two days ago, so the memory is still fresh. Let's hope it's a real memory.

Facts

1. The wooden horse spent enough time in Vegas for it to acquire the radioactive signature
   Therefore, we can assume that the wood itself was brought over from Vegas.
2. K was implanted with a real memory of the horse and furnace
   Whichever child it was that lived the furnace scene actually lived it and physically possessed the horse.

Summary

Given these, we can gather that Deckard carved the wooden horse in Vegas. Perhaps Deckard and Rachael spent some time in Vegas, before whatever happened to it. Deckard tells K:

[Vegas] was a place where you could get a drink, have a dance... gamble a little.
_{-Paraphrased from memory}

He speaks fondly of Vegas as though he and Rachael spent a good amount of time there. Perhaps there was too much heat in Vegas to keep a pregnant Replicant, or the event that caused the radiation sent them into hiding with Sapper.

After Rachael's passing and the birth of the child, the wooden horse was sent with the kid into hiding. Yes it's a huge risk to have done, but it gave the kid something to hold on to. K's memory of the horse was:

it was all the boy had, so he fought to keep it.
_{-Paraphrased from memory}

How or why did K end up with the memory of the horse if he was in fact a Replicant? We can safely assume that Stelline seemed to instill her own memories into Replicants sporadically to increase their realness, which is what seemed to give her success^[1]:

every artist puts a bit of themselves into their art
_{-Paraphrased from memory}

It can be assumed that it was a coincidence that K also had this specific memory.