says...

I was just outside watching a pass of the Cosmos 1844 Rocket satellite
when, just as it was approaching its highest altitude in the SE, I saw
what appeared to be another satellite. It was above the Cosmos, and
moved almost directly in a NW to SE direction (i.e. almost straight
down from my vantage point) but disappeared after about 10 degrees of
motion.

Extremely belatedly, I come up with Cosmos 389 as a pretty good
candidate. That's NORAD 04813, International ID 70-113A. It was
above the Cosmos 1844 Rk, moving down to the SE and went into the
Earth's shadow. Here are elements for the two objects from close
to the date of the observation:

Cosmos 389
1 04813U 70113A 03176.21405067 .00049953 00000-0 44221-3 0 6948
2 04813 81.1274 66.1923 0003679 243.2403 116.8561 15.68403042768485
Cosmos 1844 r 10.4 3.9 0.0 3.9 v 18
1 17974U 87041B 03174.76129698 -.00000190 00000-0 -70929-4 0 2784
2 17974 71.0073 225.9430 0015736 270.4608 89.4706 14.16769328833197

Ed Cannon - - Austin, Texas, USA
(Remove "donotspam".)
http://wnt.cc.utexas.edu/~ecannon/satellite.htm