router checks destination mac address

[aureliolc]

For example, 

When router A sends a packet to its next hop router B, router A will send the packet and encapsulate it in a frame with destination MAC address of router B (checking its ARP table). When router  B receives the frame, it will directly desencapsulate and check layer 3 address? or first it will check if the destination MAC address is correct?

[Reza Sharifi]

Hi,

router consults its routing tables to determine if the destination IP network is
known. If the router is directly connected to the target network, it can send the packet on to the target. The router decrements the IP header Time to Live value and then creates and applies a new MAC header to the packet before forwarding it.

HTH