Yes. Aero HF 585B is just Castrol's name for that particular oil. Their Product Data Sheet states that it meets MIL-PRF-5606H, JSD OM-15, NATO H-515, and DEF STAN 91-48/2.
Of course, if this intended for use in airworthy equipment, you should first contact the manufacturer of the equipment as MIL-PRF-5606H may not be the relevant specification for your hydraulic system.