Printing system, print management server, communication relay device, and recording medium

A non-transitory computer-readable recording medium for recording a program that causes a computer built into a print management server provided outside a predetermined LAN to execute the steps of:

• a) accepting a print output instruction from a communication terminal of a user, the print output instruction being given to a print output device provided inside the predetermined LAN and being an instruction to print out a print target file;
• b) determining whether the print target file is present inside the predetermined LAN;
• c) when it is determined that the print target file is present inside the predetermined LAN, transmitting a generation command to a communication relay device inside the predetermined LAN, the generation command being a command to generate print job data on the basis of the print target file acquired by the communication relay device and a print setting instruction;
• d) when it is determined that the print target file is not present inside the predetermined LAN, acquiring the print target file and generating print job data on the basis of the print target file and the print setting instruction;
• and
• e) when transmitting the print job data, not the generation command, causing the communication relay device to transmit the print job data to the print output device.