longevity, congratulations
壽 centers on a long, celebrated life: longevity and the congratulations that come with it.
壽 is the traditional form of 寿. It combines 老 (old age) with a phonetic component that also suggests long duration. The modern simplified form 寿 replaces the complex lower part with 寸.
The top part looks like an old person 老, and the bottom has 口 and 寸, like a mouth speaking measured words of celebration. Picture an elder being congratulated for a long life.
For ジュ, imagine a long-lived jewel (ジュエル) being presented at a longevity celebration: jewel -> ジュ, and the congratulations shine like a gem.