You are conflating two different things. 1) The two stone tablets of the Ten Commandments were given by God to the Israelites (Exodus 31:18) and kept in the Ark (Exodus ch.25), and their location is no longer known.
2) Synagogues sometimes display portrayals of the Two Tablets, but this is not a requirement, and many synagogues do not have this symbolic replica. Those that do, may make them out of wood or any other material. Actual stone replicas are not common.
Stone tablets
Stele
Moses carries stone tablets which contain the Ten Commandments from God. The number of tablets varies with each version of the story, but it is usually only one or two tablets.
Tablets of stone.
clay tablets
stone tablets
Because of its honor, the Torah scroll is not just left laying around. Housing it in a special cupboard (ark) is a sign of respect. It is also reminiscent of the Holy Ark in which the two stone tablets, given directly by God, were placed.
The ark is used for holding Sifrei Torah, the scroll held sacred by the Jews.
to text
Moses
The foundation stone for the Great Synagogue was laid in 1842 and the building was consecrated on 2 April 1844. For more information on the history and development of the Great Synagogue, see the link below.
The first books were on stone tablets and they wrote them with chisels engraved on to the stone