？
Is it true that passing your cold on to someone else cures it?
Literal
Cold [object-を] person [to-に] pass [conditional-と] get-better [quotative-って] true?
Japanese folk belief — passing a cold to someone else is supposed to cure you of it. 移す ('to transfer') collocates with 風邪 for contagion. The conditional ~と gives a natural-consequence reading ('whenever X, Y follows'). って is the casual contracted quotative (= と), framing 治る as the content of a claim being asked about. The copula is dropped before 本当, leaving a casual rising-intonation yes/no question.