The basic requirement for a router to work with BTMM is that it fully support either NAT Port Mapping Protocol (NAT-PMP) or Universal Plug and Play (UPnP).
Linksys has produced five different versions of the BEFW11S4. Some support UPnP and some do not. Look at this page
, identify your specific model, download the user manual, and check to see whether it supports UPnP. If it does not, then the router will not support BTMM.
Even if it does support UPnP, it may not fully support all UPnP functions. It is not on Apple's list of routers that work with BTMM, which I linked to in my first post. It think it is very unlikely that you will be able to use this router with BTMM.