Do you know how the tsuka strap is attached to the fukuro? Also, how does your friend use that wooden washer to keep the slats aligned?
The strap on mine appears to be a tab that was woven into the seam. I can't speak to much about fukuro construction. The Yagyu-kai used to get them handmade from a fellow in Nara, but it appears he's been getting on in years and is all but retired, so now everyone gets theirs from a variety of different sources, with slightly different designs.
Due to the natural tension in the bamboo, once the slats are cut and rounded off they naturally snap toward each other. The fellow I know simply sticks the wooden washer between the slats. The natural tension keeps the washer in place, and the circular shape keeps the slats aligned. He uses it when the shinai are out of the fukuro.
Regarding fukuro-shinai maintenance: they don't require much. After use inspect the shinai for cracks or breaks in the slats. They can be repaired using vinyl tape. When the splits in the bamboo start to reach further down, loosely
wrap vinyl tape from just where the fukuro begins to roughly halfway up. It took me a while to figure out just what "loosely" meant, but it means that there's a lot of give in the tape. When you put the fukuro back on, the tape will fold in places. I'm not sure of the exact physics, but as I understand it this will help reinforce the bamboo without putting too much stress on it. Wrapping the tape too tightly will make slat more likely to break in that area.
Repeated use will cause cracks and wrinkles in the fukuro, so it should be re-lacquered every few months (longer or shorter depending on how much you use it). If you take it off the shinai and it "wilts", it probably needs another lacquer coat. (The color of choice among Shinkage Ryu practitioners is Kamakura red, but this can be faked by mixing red and brown.) This is an important safety tip, because if the fukuro is weak, and there's a lot of strength put in the hands when cutting, the shinai can bend right around a blocking shinai and hit the other person. Along those same lines, fukuro shinai are of course flexible, but if you see it wagging up and down when doing suburi, you're using too much hands and not enough hara