The item in the picture above is from a UK company called
CableMatic but there are probably similar items on Ebay, the problem with the continuity won't be in the converter (I'm presuming the 4 connectors are in the same order from 2.5mm to 3.5mm), the problem maybe that you are connecting two things together that were never designed to communicate with each other, an example would be trying to connect a TV HDMI connector to a TV RCA composite video connector, they are incompatible formats
EDIT
There is an adapter on Ebay US
(Click HERE)