Yet another HDMI to DVI question

I own an Optoma HD79 projector with a DVI input. I already have a DVI cable going from the projector to the equipment rack.I don't want to fish a HDMI cable.

Here's the question, can I simply put an adapter on the end of the DVI cable at the equipment with a male HDMI and then plug that into my receivers monitor out ?

The adapter I bought is female DVI to male HDMI


KG

This would be a cheaper and less laborious than refishing a 20' HDMI cable.I had heard of compatability issues with DVI and HDMI. My system is pretty simple.I have a HDTV/DVR and an up converting OPPO DVD player.

KG