IP Routing - For Office Move

When a host tries to access another host in the same subnet, it issues an ARP request for the host MAC address. If no ARP reply is received, then the host is declared unreachable.

So, therefore you need a L2 VPN between the locations. The VPN server at each point will work as a bridge. It knows which MAC address is at which side of the VPN connection, and will relay traffic to the other side as needed. OpenVPN bridge mode is good for this.

I think you may be asking the wrong question... (X-Y Problem)
It should be:

"How would you recommend I move the IT infrastructure to a new location?"

or

"What factors should I consider in planning a office move?"

Ideally, you could accomplish the move in one shot. There are moving firms that specialize in this, and it's not an uncommon thing.

I've been part of full datacenter moves, multiple facility moves and plenty of small office migrations to a new location.

But, if you don't have the option of making this type of move in one step, consider your applications, networking and other constraints.

VPN is a common approach if you have internet connectivity established at the new location. Make a temporary new subnet, relocate servers as needed. Use DNS to manage how end users connect to the systems.

If the sites are close, you have some easy wireless bridging options.

VPN bridging is an option as per the other answer. Do you want to share any information about the type of firewalls you have in place?

Granted, we don't have any details of what your critical applications are, the inbound/outbound requirements, NAT setup, DNS status... So that's a little tough to condense into one answer.

If an address is in the same subnet as the sender then the sender will not generally send it to the gateway. It will arp for the destination address and if that fails it will generally give up.

There are two practical soloutions to this.

1. Run a layer 2 VPN so that you have a virtual Ethernet network spanning the two offices.
2. Use proxy arp so that the gateway router pretends to be the destination and can then pick up the traffic and route it.