Is it possible to ferment milk Kefir using water Kefir liquid?
No, you cannot do that. Unlike other cultured dairy products like yogurt, kefir needs both the right bacteria and a fungus to ferment. The liquid will have the bacteria, but the fungus "mother" - the kefir grains - will be missing. To make new kefir constantly, you really need to keep kefir grains, and specifically milk kefir grains. 

If you only make kefir rarely, there is the option of buying dried kefir culture, which contains a sufficient amount of ground grains to give you fermented kefir without the need to breed a grain colony that needs to be kept alive permanently. But if you want a supply of kefir, the cost effective option is to breed the grains.