Create a transit gateway. Create a Site-to-Site VPN connection between the on-premises network and VPC B, and connect the VPN connection to the transit gateway. Add a route to direct traffic to the peered vpCs, and add an authorization rule to give clients access to the VPCs A and B.

Update the route tables for the Site-to-Site VPN and both VPCs for all three networks. Configure BGP propagation for all three networks. Wait for up to 5 minutes for BGP propagation to finish.

Modify the Site-to-Site VPN's virtual private gateway definition to include VPC A and VPC B. Split the two routers of the virtual private getaway between the two VPCS.