Hi!
Look at the aruba transceiver guide:
https://support.hpe.com/hpsc/doc/public/display?docId=a00028947en_us
The datasheet say's that the transceiver is working at 850nm up to 550 m or 1804.46 ft.
If you compare it with the cisco SFP Module Datasheet, I guess they will match.
There are no explicit statement to the GLC-SX-MMD, except it can be operated in extended temperature range.
But the GLC-SX-MMD belongs to the 1000BASE-SX Class transceivers.
cisco:
aruba:
For none of the two transceivers are OM4 values listed.
But they operate on 850 nm, so they should work together.
I had J4858D on OM4 fibers working, but not in connection with other vendors.
On OM3 lines, I saw aruba and cisco SX transceivers working together.
Sometimes, older cisco routers need to be set to 1Gbit fixed speed to come up with other vendors.
I conclude out of the datasheets that it should work.
But I can not guarantee it for you, maybe your partner can provide you test equipment to be sure?