They all share the ethical intention ------ safe transference.
What preposition is the most idiomatic to put in the blank? "to", "of", "for", etc.?
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The preposition that is appropriate here is of.
They all share the ethical intention of ...
This is [some thing] in relation to [some other thing] (a noun) and could be written as, "They all share the ethical intention in relation to [something]."
If the [something] was an action (i.e. verb), then the preposition could be "to". For example, "They all share the ethical intention to transfer the money safely.", or (more idiomatically) "They all have the ethical intention to transfer the money safely."