It's not clear from the FAQ if trading items between investigators can take place outside of the Movement phase ("before, during or after movement"). A loose interpretation would suggest this. On the other hand, I recall the Coded Messages condition card lets you trade Clues like items but only during the Movement phase, so it wasn't clear if the card was to imply that all items could only be traded during the Movement phase.
I'm just wondering since the Innsmouth rules FAQ section explicitly makes clear you must flee/engage in combat with an on-board monster during the Arkham encounter phase, in the event you get a "go to another Arkham location and immediately have an encounter there" encounter. So if the editor of the newspaper drives me to the Woods, and my fellow investigator has hidden from the Ghost there, can he give me his Cross before I execute the flee/fight sequence with the Ghost, even though it's technically the Arkham Encounter phase and NOT the Movement phase?