A down-and-out and very hungry man finds a "nut" on the street, practically breaks a tooth biting down on it, and accidentally swallows it. It isn't really a nut, but an alien matter transmitter, and his bite has triggered the mechanism to "send." Fortunately, the transmitter has a safeguard not to send living tissue, but as long as it is lodged in his stomach, any food that the man eats is transmitted to the aliens' planet. He bums some food and is even hungrier after eating it than he was before. He enters an eating contest and wins handily, complaining that he is starving.
Meanwhile, the aliens, a cheerful male and female couple who are exploring Earth, relocate their missing device after some anxious searching. Just in time, because their colleagues back on the home planet, perplexed by the repeated transmission of Earth food, have sent them a shipment of alien melons. Suddenly the poor man's belly is bulging and he is in terrible pain.
Well, it all turns out right in the end. The alien couple are content to leave the transmitter where it is as long as they can control it, and they not only give the poor man a job, but cure him of his ailments and educate him. By the time they are ready to leave Earth, removing the transmitter first, the man is in great shape physically and mentally.
This was a mildly humorous short story that I read in an English-language anthology. I don't recall when I read it, but the style was somewhat old-fashioned, which means it was most likely written during the 1940s to 1970s.