lol, check out how I got the star in "bouncing side by side" (spoilers)

[ZIGS]

So you know the star on top of that structure near the huge pyramid, right? I got there but brought along a jammer from another puzzle. You can barely see it in this screenshot:

http://cloud-2.steampowered.com/ugc/535131928321273344/9DB7237BDBAF2BC125E48665A675908F2A6BF9C2/

Then I just pointed it at the door blocking the start in bouncing side by side and voilá, hehehe:

http://cloud-2.steampowered.com/ugc/535131928321258367/8D82AC4F489992FF135C8CA79E424DF1C71C1A78/

I can't believe it actually worked given the huge distance but it did

[Riv]

I stole a box from that puzzle where you have to ride the bombs, was the most straightforward imo.

There are some cool things you can do by pointing stuff between the puzzles, and some of them weren't intended. IIRC in one of the first puzzles where you get the recording feature and simply have to pass through a few force walls, you can disable one of them with a Jammer from across the area, but it doesn't change much since you have enough ways to open walls already. Also I found unused connectors/cubes in some puzzles where you can save on them with a better connector placement.

[Grey Heron]

Doing stuff that crosses between puzzles is weirdly entertaining. My favourite I think is C3. When opening the ice cave, I found a solution that took two connectors... then proceeded to redo it using every connector and puzzle on the map, despite this being absurdly inefficient.

(I also solved "Big Stairs, Little Stairs" with the aid of lasers and jammers from other puzzles)

[Kein Zantezuken]

I have no idea what puzzle you are talking about and screenshots do not help.

Either way, taking things out of one puzzle room and bringing into another isn't that uncommon. Just not always worth it.