I found two Une Livre (one pound) bank notes from the Banque de Syrie et du Liban (Bank of Syria and the Lebanon). They were printed in Damascus in 1939. The two countries located in the Syria mandate territory shared a currency then and in the year 1939 the currency was just being split into two (which remained interchangeable). This process was similar to the development of the Palestine Pound in Israel and Transjordan.
The notes looked identical for Syria and Lebanon:
The back is the same for both versions:
I am still looking for Iraqi money from the mandate time. I get my artefacts from Israel and find it difficult to find things from Transjordan and Iraq. I assume there was not much business between Israel and Transjordan (no Jews) and Israel and Iraq (no direct railroad link) compared to Israel and Syria/Lebanon and Israel and Egypt.