Ok, I've found a few additional articles in the Guardian that hopefully shed a little more light on the construction process at Prestbury.
The first is an announcement on May 6 1920 that "an ambitious scheme for a new golf club in Cheshire is making rapid progress.....Mr H. S. Colt has inspected the land and his report is most favourable." No mention of Mackenzie at this time.
Then comes the October 21 1920 article included at the start of the thread which does mention Mackenzie assisting Colt.
In the October 3 1922 issue they report on progress with "the new Prestbury Links........the holes were planned by Mr H. S. Colt, whose work probably gives more pleasure to players than that of any other British links architect." Again no mention of Mackenzie.
By November 23 1922 the course hosted a professionals vs Amateurs match and the report concludes with "When the fifty odd additional bunkers, recommended by Mr. H. S. Colt, have been added the links will be second to none of the inland greens in the North of England." So it would appear that reports that the course was not fully 'completed' when it was opened - here it is reported that Colt will be adding some fifty bunkers which suggests that not many were built when the course was first opened. I wonder why?
Then, by January 30 1923 a report on an interesting test for 4 selected professionals who were picked from the 60 who had applied for the new post of professional at Prestbury. A playing test so to speak. The guy who came second won the job! The report states that, "The course was in excellent condition. Already, many of the hazards, designed by Mr. H. S. Colt, the architect, have been arranged, and the players dropped numerous strokes on the greens, which were fast and tricky." Once more, no mention of Mackenzie.
From these reports there is only one mention of Mackenzie and so it would appear that the likely scenario is that Mackenzie may have undertaken one or two inspections to help out his partner but the lion's share of the credit should go with Colt naturally.