So basically, router B is wired to the LAN of router A? Is that correct?
First you should setup router B to run as access point only:
- assign a non-conflicting LAN IP address to router B, e.g. 192.168.1.2 instead of 192.168.1.1.
- turn off the DHCP server on router B
- connect a numbered LAN port of router B with a numbered LAN port of router A
- do not use the Internet port of router B. It remains empty.
- ignore the internet connection settings in router B.
Now router A is the gateway router for your LAN. It also runs the DHCP server for your LAN. Wireless client connected to router B will get their IP address from router A and use router A for internet connection.
Then you should be able to setup a roaming network with these two routers. For this, both routers must basically have the identical wireless settings except for the wireless channel which should be different to avoid interference. Thus, set the same SSID and the same wireless security settings on both routers. If you use MAC address filtering you have to set it up on both. Assign different channels on both routers, e.g. 1 and 6.
With this setup a wireless client should be able to roam between both routers. When the connection to one of the routers gets too weak and the other one is in range the wireless client should automatically switch to the other one maintaining the connection. Some wireless cards have difficulties with roaming so it may not always work perfectly with all devices.
See also Linksys FAQ
ID 622.