Incredible that Emirates has driven pilots to Pprune for an opinion, least we should do the wrong thing.
Your logbook, log what you want. Personally, I log the lot regardless of wether I am PIC or augmenting. Either duty I'm in the bunk for part of the flight so I find it bizarre that as PIC I can log all, but as augmenting I allegedly can't? Company records can reflect what they like (as FO or Captain) but my logbook reflects my personal choice. If another airline wants it all, I have the record. If they don't, I'll take it out.
Fuse Plug, buy an e-log book. Much easier.