The convert button has no real purpose for a desktop computer. The idea is that you scribble some words there with a pen or mouse and it converts it to words for you.
It was originally in MSN Messenger for PDA's: it would make sending text easier. The handwriting plugin simply enables the function (by faking Messenger it's running on a PDA). Since it would have no use to use converting on a normal PC, Microsoft hasn't put it in the normal PC version if Windows.
However, if you wish to make it work, you can take a look at
Convert Tab and
Using "Convert" in a non-TabletPC !!! 
Convert in Handwriting plugin
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