DDMunday, if you want to try to confirm your mother's iris is Immortality I would recommend purchasing a rhizome of Immortality next year from a reputable vendor. Plant it in close proximity to your mystery iris.
See if the growth habits match (same general size, shape and color of foliage). See if the two plants bloom at the same time. Closely compare the blooms and fragrance, if any. Look carefully at the beards. Are they identical?
Also compare the bloom stalks and bud spacing. The more details that line up the more likely you have a match.
Good luck!
Randy