Should he prioritize traveling to see his elderly mother in her home country, or should he prioritize the job opportunity offered to him, delaying the trip until next year?

Your friend is permitted to postpone his visit to his mother until next year, especially given his urgent need for work and the presence of another brother who looks after his mother's affairs. He should utilize means of communication to check on her. Righteousness towards parents and maintaining kinship ties have not been assigned a specific limit by the Sharia, and communication in this case is considered a form of righteousness and connection.