Did something similar. Bought a RJ45 connector with female sockets on both end. Plug a RJ45 terminated cable to 1 side, then RJ11 terminated cable to the other and you get a long wire with RJ45 plug on one side and RJ11 plug on the other end.
If not in a hurry can get from ebay
http://www.ebay.com.sg/itm/RJ11-6P4C-Female-To-Ethernet-RJ45-8P8C-Male-F-M-Adapter-Converter-Cable-White-/331863731656?hash=item4d449eadc8:g:VwMAAOSw9GhYbgrY
Lazy to search in Sim Lim Tower, so previously I bought a few from taobao
https://item.taobao.com/item.htm?spm=a1z09.2.0.0.CXFnCr&id=522665056391&_u=p29jlne46655
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