Say a source sends a packet to its destination via router A and router B.
In the forwarding table of router A, it will only have the mapping between the IP address of destination and that of one of its own interfaces (egress interface). We do not know the IP address of ingress interface of B.
Given the fact that ARP must know an IP in its own subnet before it translate IP address to MAC address, how Link Layer at egress interface of A will be able to look up the MAC (or equivalent) address of the ingress interface of B?