To avoid re-authentication their would have to be sufficient coverage that the connection would not drop when moving between the two buildings - in this the case?
Obviously the SSID needs to be the same in both buildings.
Next, do the two buildings share the same layer 2 vlan (and are connected at layer2)? If so, bridge the SSID in each building to that same VLAN.
Failing that, are the two buildings connected at layer 3? If so, use layer 3 roaming rather than bridging - but the result is not as perfect.