I finally managed to complete it! Didn't even know it's possible till now :D
Just carefully break the rib chest (i did it with hammer), remove everything, lungs too. Then cut the veins leading from the original heart with one of the scalpels laying around and then put in the new heart. The veins will join themselves i think.
SURGERY COMPLETE
"Looks fine to me, I'm sure he'll live..."
Final blood level: 4271.467 ml
Surgery time: 5:23
Rating: A++