Do producers produce organic matter from existing organic matter?

No

Organic matter is what life is made of - this means that some of that life are producers and some are decomposers (and some are consumers).

Organic matter (or organic material) is matter that has come from a once-living organism; is capable of decay, or the product of decay; or is composed of organic compounds. The definition of organic...

Usually carbon-based substances derived from living things. Examples include everything we grow and eat, wood, dung and the humus content of soil. Organic matter can be added to soil to make it more...

Fuel