Let's say I, as a Kohen, would receive terumah.
Would it be permissible for me to give the terumah which I have received to the poor so that they may consume it despite not being kohanim?
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A poor person cannot eat Terumah unless he is a Kohein or part of a Kohein's family. Poverty doesn't help in any way. (See Rambam Terumot 11:27 for a similar case.) (You can give a poor person Demai (Rambam Maaserot 10:11), but that isn't what you asked about.)
If you want to be nice though, and the poor person is female, you can marry her so she can eat it. Once during a famine R Tarfon did just that and married 300 women in order to feed them Terumah (Yerushalmi Yevamot 4:12).