I think you can move it like the Sharks did IRL with their 2019 and 2020 1st round picks. Ottawa got the 2019 1st if Buffalo got the 2020 1st. Ottawa got the 2020 1st if Buffalo got the 2019 1st.
That depends on the conditions. Some conditions specify which team's pick must be transferred, some specify the better (or worse) of multiple picks, some leave multiple picks as options (2019 or 2020, for example), and some simply do not specify ("a
" 2019 1st is either insufficient information available, or at the discretion of one of the teams).
*Conditions: Pick upgrades to a 2019 1st round pick if Sharks re-sign Kane. If Sharks don't make the playoffs in 2019, then Sharks have the option to retain the 2019 1st and Buffalo receives a 2020 first round pick instead.
*Conditions: Ottawa receives Sharks 2019 1st round pick if Sharks do not make the playoffs. If Sharks make the playoffs, Ottawa receives Sharks 2020 1st.
*Result: Sharks made the 2019 playoffs, Ottawa receives Sharks 2020 1st round pick
What happened here, was separate conditions attached to the same pick. Not multiple picks which could change based on conditions.
If SJ did not make the playoffs, they had the option of giving Buffalo their 2020 1st round pick, which would allow them to satisfy the other condition attached to their 2019 1st and send it to Ottawa.
If they did make the playoffs, Buffalo receives the 2019 1st and Ottawa receives the 2020 1st.