KanjiJLPT N3
Exist

exist, suppose, be aware of, believe, feel

Mnemonic

napoleon drives a stick deep into the earth and kneels before his child: "You will exist beyond my reign." The child grabs the stick, and as long as it stands upright, the dynasty exists — preserved through the ages.
Additional thoughts
Picture Napoleon on a battlefield, planting a stick like a flag, then placing his child's hand on it. The stick is the anchor of existence — while it stands, the child's line endures. Vertical stick runs through the whole kanji, binding Napoleon on top to the child below.
Quick recall
napoleon plants a stick for his child, ensuring the bloodline will exist forever.

Details

The keyword for 存 is exist. This kanji conveys the fundamental concept of being, existing, or continuing to be present. It carries the sense of something being preserved, maintained, or kept in a state of existence over time. By extension, it can also relate to knowing or being aware of something's existence, as well as the idea of survival or preservation.
On'yomi
そん、ぞん
Kun'yomi
ながら.える、あ.る、たも.つ、と.う