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If yes, at which maximum distance?"
For sure at the very same maximum distance capable when using tested OM2 MMF cables (50/125 um 850 nm), so up to 550 meters.
That's to say that using OM3 MMF or, better, OM4 MMF cables helps enhancing overall performance of optical signals and, probably, considering that, a valuable length can unofficially gained over the official 550 meters threshold value...but not so long (at some point shifting to SMF over MMF become a must if you have a long run) and nothing in that territory, in term of admissible official working values, should be taken for granted (somewhere -
here as example - I saw reported a maximum distance of maybe 800/1000 meters, at best...and those values are not related to an Aruba SFP 1G SR Transceiver...indeed those values are not coming from something tested and declared by Aruba as per published standards...and indeed Aruba doesn't report those values too, see
here a discussion about what is granted and what's not on MMF with SFP SR Aruba Transceivers).
A 300 meters run, especially deployed with OM3 MMF, should be an easy run for two J4858D so I believe you can expect 1Gbps Full Duplex without issues if optical cabling and patches is correctly deployed, tested and so certified.