I realize this came from an old collection with no data. However, one helpful test to make to help identify the green mineral is to place a drop of vinegar on it to see if there is any fizz reaction. If so, the mineral is probably calcite. 

I'm going to take a stab at identification in the meantime- at first I thought this was a drill core sample, but it looks like it has a tapered shape, with one end having a larger diameter than the other. Also there are some irregularities on the surface that possibly point to this being a fossil, perhaps of a cephalopod. The rounded, smoothed end, if not artificially polished resembles the distal end of a cephalopod. The item itself lacks evidence of an actual "shell", so it could be a relict mold of the original fossil. See attached link for further details and description. 

Cheers,

Holger

Thanks for the video. It provides a better view. I would suggest testing the hardness next. Use the point of a steel knife or pin and try scratching the green mineral in a small obscure area (so you don't noticeably damage it) as well as the brown host rock. I noticed on the video that the smooth, rounded end seems to be a distinct darker brown layer. Test that as well.

With regards to the vinegar test, sometimes the reaction is subdued, so you could try repeating it using pickling vinegar which is more concentrated. The usual test is with dilute hydrochloric acid, but if it scratches with the knife and you see a reaction, it is likely calcite. Check the host rock for a reaction as well.

Kyle

Since the materials are softer than your steel blade we can rule out quartz/chalcedony as the greenish mineral. The lack of a fizzing reaction with vinegar would rule out calcite and most other carbonates bit it would still be worth confirming that with a stronger vinegar or dilute hydrochloric acid (muriatic acid). Try the vinegar/acid on an area after you've scratched it to test the powdered material. If it is a "pipe blockage" type material, I would expect it to react with vinegar. If there is still no reaction, then it becomes a much more difficult exercise for identification via this forum. You may be best off to take it to a local rock club and seek out someone knowledgeable who can assess it first-hand.