Since charged Runes can't be moved to the vault nor to another character, please move them to the Mission slots at the bottom of the inventory screen.
Runes aren't really materials to begin with, and they take up too many slots - Reciprocal, Stolen and Antiquated runes take up 3 Materials slots per character. For someone with 3 character, they take up 9 slots that could otherwise be used to store something else.
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They could always stack the runes instead of having them take 1 slot in your inventory.