That green plants can produce their own food by photosynthesis using sunlight is common knowledge. But if someone claims that an organism can acquire the ability to photosynthesizes simply by eating plants one would laugh at it. Is it true?

no, simply by eating plants an animal will not be "converted". That doesn't mean though that interesting associations cannot occur, although I am hard-put to think of one involving an animal and a plant at the moment. Certainly some plants that cannot photosynthesize use others that can and form a frequently but not always mutually dependent or beneficial permanent bond.
Another question is of course COULD it occur.... never say never. There are some odd examples (or in the view of some, odd theories) that show that a coming together of two organisms at the cellular level can or could result in one single independent organism from then on. Margulis's Endosymbiotic Theory is a nice example of that. Might not seem much, two cells but... those cells multiplied together make you and me, animals, plants.... if she was right (she was very pretty and married to Carl Sagan but that isn't quite enough evidence..