There are well-known monomorphisms between the Artin groups of finite type An, Bn=Cn and affine type A˜n−1, C˜n−1. The Artin group A(An) is isomorphic to the (n+1)-strand braid group Bn+1, and the other three Artin groups are isomorphic to some subgroups of Bn+1. The inclusions between these subgroups yield monomorphisms A(Bn)→A(An), A(A˜n−1)→A(Bn) and A(C˜n−1)→A(Bn). There are another type of monomorphisms A(Bd)→A(Amd−1), A(Bd)→A(Bmd) and A(Bd)→A(Amd) which are induced by isomorphisms between Artin groups of type B and centralizers of periodic braids.In this paper, we show that the monomorphisms A(Bd)→A(Amd−1), A(Bd)→A(Bmd) and A(Bd)→A(Amd) induce injective functions on the set of conjugacy classes, and that none of the monomorphisms A(Bn)→A(An), A(A˜n−1)→A(Bn) and A(C˜n−1)→A(Bn) does so.