The abstract noun "investigation" can be expressed with the verbs "investigate" or "search." Alternate translation: "ordered his officials to investigate" or "ordered his officials to search" (See: [[rc://en/ta/man/translate/figs-abstractnouns]])
What they were to investigate can be stated clearly. Alternate translation: "ordered his officials to investigate the records" or "ordered his officials to search and find out if there was a record of King Cyrus telling the Jews to build the house of God in Jerusalem" (See: [[rc://en/ta/man/translate/figs-explicit]])