Christ is born to fulfil the Law. It is Christ, Priest in the order of Melchisedech, who finally fulfilled the Law by offering His Body for our sins on Golgotha (Lk 24:44-49). As the Jewish Temple Cult is the subject of the Law, this fulfilment must be linked to the Old Testament Temple Cult and so the H. Mass either. Therefore, the fulfilment of the Law must follow Exodus in its context of the "Exodus from Egypt, the land of slavery".
This fulfilment of the Law did not start with Christ hanging on the Cross, Christ standing before the Sanhedrin or Christ instituting the Eucharist at the Last Supper or something like that, but with His Conception and Birth: "He was born to fulfil the Law". The Birth of the "Innocent Lamb of God" that was born in the "Stable of the City of David", Bethlehem, i.e. the stable of the lambs usually destined for the Paschal Sacrifice. Therefore the Shepherds of this stable were the first to be informed by the angels about the "Birth of the Lamb of God" in their stable. And as it began with the Conception and Birth of the "Lamb of God" it ended with the sacrifice of the "Eternal Lamb of God" on the cross after which His glorious resurrection and ascension could take place.
This process of fulfilment follows the Law as given in the Old Testament Temple Cult. Without claiming to be complete an overview of the fulfilment is given here in its main points as follows:
Thus "a holy priesthood" who "offer spiritual sacrifices acceptable to God through Jesus Christ" (I Peter 2:5) during which the ordained priests "in Person of the High Priest, Christ" offers the Passover Lamb and then "in Person of the High Priest, Christ" eats first of the Passover Lamb as Sacrificial (Spiritual) Meal, after which the faithful as a "holy priesthood" follow. This is the one, true and eternal Sacrifice of the Eternal Passover Lamb, who is unblemished and appointed "scapegoat" He is bearing our sins. In this way Christ used the context of the Passover as a Memory of the "Exodus from Egypt, the land of slavery" and through the associated "Yom Kippur" for a paradigm shift into a commemoration of Christ as a Memory of the "Exodus out of the land of slavery to sin" of which He is the door to Heaven.
The institution of the Eucharist by Christ at the Last Supper was on the Thursday evening. This Last Supper could therefore neither be a Sabbath meal, as suggested by the new Offertory prayers of the 1969 Reform, nor the Sacrificial Passover Meal of Pesach. It was one day too early for it. Rather, it was the first meal of the 14th day of the first month when the 7-day Feast of the Unleavened Bread began. Whereas the Unleavened Bread signifies being unblemished (I Cor. 5:7, I John 3:5, Hebr. 7:26) in contrast to the leaven bread that stands as the common symbol for Sin (Amos 4:5, Hosea 7:4, Lk 12:1, Matt. 16:6-12, Gal. 5:9, I Cor. 5:6-8). So, the Last Supper was the first Passover Meal at which the symbolic Unleavened Bread was eaten in the evening before the Sacrificial Passover Meal. It was from this meal that Christ used the symbolic Unleavened Bread and Wine for a paradigm shift into His innocent and unblemished Body and Blood. That is why Christ had to institute the Eucharist at the Last Supper by commanding the apostles, "Do this in remembrance of me". With "Do this ..." He did not command them to repeat the Last Supper, but to repeat His Acts in union with and in commemoration of His Sacrifice on the cross as the ultimate fulfilment of the Law: "He took the Bread and blessed it", "He took the Cup and blessed it" (= Offertory: taking Bread and Wine from profane use to prepare them by offering it for sacred use), then "He consecrated both, Bread and Wine" (= Consecration) with "the Remembrance" (= Anamnesis), after which "He broke the consecrated bread" (= Fraction) and finally "he gave to eat the consecrated bread and wine, his flesh and blood" (= Communion as the Sacrificial/Spiritual Meal).
The institution of the Eucharist, therefore, does not refer to the Last Supper, but to the Sacrifice of our Lord as the innocent Lamb of God bearing as Scapegoat our sins. As such, the Eucharist is the same true and eternal Sacrifice for our sins in which Christ ultimately fulfilled the entire Old Testament Temple Cult. Mystically, the Eucharist at the Last Supper, preceding the Crucifixion, as well as all those taking place since then at each H. Mass by Christ in His "Mystical Body" is one and the same as the physical Sacrifice at Golgotha, It is Christ, the Eternal High Priest, who offers and sacrifices Himself on the cross for our sins.