Let $A,B$ be sets and $G,H$ be order-relation for $A,B$ respectively.

Say, i proved existence of an isomorphism $\psi$ such that [$(x,y)\in G$ iff $(\psi(x),\psi(y))\in H$]. However, "$A\cong B$" gives no information about which order relations these sets take.

Is there a notation includes information about given relations?