Armenian stamps, created by applying handstamped overprints on Tsarists stamps, were used as base stamps for issues in Georgia and Transcaucasia. A further overprint was applied to create a new issue.
In case of the Transcaucasian issue in April 1923 a star overprint was used.
The stamp shown features an E.6 type framed Z overprint. On the back side is a genuine mark of the Soviet Philatelic Association which shines through at the lower right corner. The stamps with the star overprints where used mostly in Baku since there was a shortage of stamps at this time. A couple of different Armenian stamps with star overprints exist. Like most material from that time the star overprints have been massively forged. The historical circumstances of the star issue (remaining stock from all three members of the Federation were requested and sent to Tiflis for overprinting/stamping) suggest that no over the counter productions or rare overprints were used. If you find unusual overprints in unusual colors, it is most likely fake.
The Georgians used Armenian stamps as part of a somewhat “enigmatic” (like Ceresa called it) issue in 1923. It probably was an emergency issue and so far has been only reported to be used in Tiflis.
One of the open questions about this issue is why the overprint is only 15.000 rubles when postal rates at this time go from 75.000 rubles for a local postcard to 500.000 rubles for a foreign registered letter [Ceresa]. The Liapin catalog (which represents Zakiyans research) as well as Ceresa only list the 15.000 rubles overprint on the 5r HH on 15 Kopeck. Other combinations are most likely fake. If you own those please send me a scan. Even if the chance is very slim, it is still possible combinations exist that were previously not known.
Here are scans I got from a reader of this blog which show unusual Armenian overprints (red ink!) and are fake.