Service position and rally movement differ
Badminton BC’s rules overview explains that doubles partners change their respective service courts when they win a point while serving. Winning a rally while receiving does not by itself cause that swap. Their movements during the rally are a different matter.
Track a pair receiving at 5–6. They win and reach 6–6 with the right to serve. Do not automatically exchange their recorded service courts because the scoreboard changed. First establish who already occupied the appropriate court for the new service.
If they then win that serving rally, the same server continues from the alternate service court. That later swap has a different trigger from the earlier receiving win.
Keep a service map rather than freezing rally positions
Players may have crossed during open play, so their positions at the last hit do not necessarily represent their service-court order. Record the order at the service stages, then apply the appropriate rally outcome.
This makes a doubles service graphic easier to follow without assuming partners take turns on every point. The original 5–6 sequence explains one transition; it does not replace the full service-order diagram for a match whose earlier order is unknown.
Questions answered
Does every won rally swap the pair’s service courts?
No.
Can the final positions during a rally replace the service-order record?
No. Track the service stages.
Sources & further reading
Official references for the subjects discussed. Service terms and device software can change.