How can all the routers remember my leased IP? Shouldn't it change if I coect to a different router?

If i have understood this correctly. The DHCP server will lease you an IP address, when you first coect to let's say a school network. If I move from the 8th floor to the 2nd floor, then I'll most likely coect to a different router. If the lease hasn't expired yet, how does the new router figure out what my leased IP is? and won't that be a little confusing if let's say i am coected to subnetwork 192.168.3.0 but have leased an IP that belongs to another subnetwork?