Below is the relevant extract from the oneworld rules. Under oneworld rules, because you are connecting from a longhaul flight to another longhaul flight, you don't qualify for F lounge access. However, CX rules are a little more flexible, and I don't think you will have any issue access either of the F lounges on production of your F and J boarding passes together with a mention of 'connecting from F'.
Connecting between oneworld marketed and operated flights:
First and Business Class customers connecting on the same day of travel, or before 6am the following day, can access the lounge when travelling between an international long haul (a oneworld international long haul flight is defined as an international flight marketed and operated by any oneworld carrier with a scheduled flight time longer than 5 hours) and an international short haul or domestic flight (and vice-versa).