US Insert for The Cabinet of Dr Caligari (1920)
That's a pretty amazing poster, and would be an incredible find.
But my first thought when I see it is that it's not real.
Philips was the name of the UK releasing company for Caligari (all the US material simply says Distributed by Goldwyn) and an insert is not a standard size they used back then.
The show dates printed on the bottom of the poster Fri-Sat March 19-21 (which would be Fri-Sun, not Fri-Sat) would be 1920 show dates, but the film debuted in Germany the last week of February 1920 and didn't roll out to other countries until 1921.
Can't find any info on a Senator Theater in the UK (and wouldn't that be a "theatre" anyways), though I do find one in Baltimore starting in 1939.
Lastly the idea that a theater was air-conditioned in 1920 would be huge, the Rivoli in Times Square usually gets credit for being the first theater to have air-conditioning and that was in 1925.