Device for rapid connection between a totally implantable heart prosthesisand natural auricles. According to the invention, said prosthesis comprises:fastening means (16, 25) for fastening an end of one of the lunettes (2, 3) to theother lunette (3, 2), said fastening means being able to permit folding of saidlunettes relative to each other; guide means (10, 11, 20, 21) for guiding saidlunettes relative to each other before and during fastening and also during folding;and snap-fit means (19, 26) for engaging said lunettes on each other in the operatingposition corresponding to the end of said folding.