Make sure your green points and connections share common ID field (say PART) with brown points. Define shortest link length (L) in each group and draw buffer around parent brown point with slightly smaller radius than L or simply very small buffer:
Find intersection points between buffer outline and connections, convert to single parts. Find script that assigns chainage to points on the line:
Using spatial join twice transfer chainage from intersection points->connection->green points.
Now you can use points to line tool (line ID = PART) and chainage as sort field to connect green points by closed line:
Note 'bad' polygons 1 and 3. Either fix them by hand by adding brown point as extra vertex or append such brown points to green points making sure that their chainage is 1mm greater than largest one in a group (or equal to 0.0) and re-run points to line tool.
Not sure that you can convert them to polygons at once due to intersections.