Unfortunately I don’t know the part number — the factory sourced all the parts and we don’t know the part number for this header. I do know its spec: it’s SMD 2×4 female pin header, 3.5mm height. If you don’t need to fit everything into the OpenSprinkler enclosure, you can use standard 2×4 female header (or even 1×4 female header as only the top 4 pins are used). This will make the LCD sit higher than expected (so it won’t fit into the OpenSprinkler enclosure, but otherwise it works just fine).