A prosthetic heart valve replacement system and method aim to reduce the time duration of the patient on the heart-lung machine during surgery. In one embodiment, the invention uses a two rings (e.g., of Titanium) comprising a first outer anchoring ring installed in a first step in the patient annulus, e.g., by stapling (e.g., using Nitinol® staples), and a second inner valve ring which has apertures and to which the sewing cuff of prosthetic heart valve (e.g., of Dacron) is sutured around the sewing cuff. The suturing is expediently completed outside of the patient's body, parallel with the stapling of the anchoring ring in the patient annulus. The inner valve ring may have circumferential resiliency. The inner valve ring along with the fastened/sutured prosthetic valve is installed snugly (in a second step) to be captively retained concentrically within the already installed outer anchoring ring, to complete the heart valve replacement.