A friend recently passed this on, thinking it sounded false. It’s actually a reasonably accurate translation of Dhammapada verse 223, which in Buddharakkhita’s translation is:
Overcome the angry by non-anger; overcome the wicked by goodness; overcome the miser by generosity; overcome the liar by truth.
The only real difference is the choice of verb: “silence” in the suspect quote, versus “overcome” in Buddharakhita’s version.
In the Pali the verb used is “jine” which is definitely “conquer” or “overcome.” It’s what’s called the “third person singular optative,” which means that it’s “one should conquer.” It’s kind of an instruction.