No, you can't Research from a reconstructed item (which you make on one character, who knows the trait, and transfer to another, who doesn't).

You also can't Research from a transmuted item.

Best you can do is Deconstruct a transmuted item, with a character that has the skills that help you get more back from deconstruction, so you have a better chance of getting the trait material. 50 Transmute stones for, say, what looks to me like a 60% chance at a Potent Nirncrux if you transmute a Weapon to Nirnhoned. Then you can reconstruct it (with a character who already knows the trait) as a real item, and pass it to your other character to research from.

Unfortunately this does not work with transmuting jewelry to Triune and deconstructing from that, since when you deconstruct jewelry, you only get a grain (of which you need 10), not a full trait material, so in order to get the 10 grains of dawn-prism to reconstruct into a full Dawn-Prism, you'd need to transmute 15-20 jewelry items on average, which would cost you pretty much all your transmute stones at once (at 50 per item, that means 750-1000 and you can only hold 1000 at once.)