Is Luke's green beard trimmer in The Last Jedi?

We need to talk about Luke's lightsabers.

Yet again.

So, let's clear this up.

Luke lost his blue lighter when his own father sliced his arm off in ESB. It fell down the shaft.

The brutal irony of this was that Vader lost the same saber to Obi-Wan Kenobi in Revenge of the Sith when he lost his own arm and legs.

Something about the higher ground, I'm believe.

Anyways, as that blue saber was lost to Luke he instead made his much cooler green saber. In a deleted scene from Return of the Jedi, you can find him in a cave adding a Kyber crystal to the device he's manufactured. It was cut because it was a way cooler idea to have the green blade be revealed when Luke catches it from R2D2's throw. See the above photo from the scene.

The blue saber eventually found it's way back to Luke in The Force Awakens where it went from Maz Kanata, to Finn and then Rey.

In the Last Jedi trailer we see Rey training on the Island with a blue saber while Luke overseas her exercise.

We can assume that Luke gave the saber back to Rey or that he never accepted it from her outstretched hand at the end of TFA.

Now, about that green saber and the end of Return of the Jedi.

After Luke has dispatched his dad's arm and red saber down the well, the Emperor offers him a new job at his side, replacing his now dying dad. Luke realizes he is now well on the path to the dark side of the Force, and throws his saber down in disgust, rejecting the Emperor job offer and giving the best quote from Return of the Jedi:

Never, I'm a Jedi like, my father was before me!

And then Emperor whips out some Force lightning and the rest is history as found the Journal of the Whills.

And then Lando and friends blew up the Death Star and along with it Luke's green saber.

Right?

No.

We didn't see it on screen but Like picked it up as he's wearing it at the Ewok Jamborree at the end of Jedi.