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The popular Bonza puzzle app is about solving these types of clueless crosswords, by moving the fragments around to form words that are linked by a common theme. The puzzle has a similar presentation and follows the same convention that the resulting grid cannot include any 2x2 clusters of tiles.
The pieces can be grouped together by colour and assembled into five interlocking crossword grids. This can be done by simply looking for arrangements that make valid words, but gets easier after a few words have been found by noting commonalities of theme within the colours (as is usual for a Bonza puzzle). Doing so produces the following result:
Considering the diagram of five interlocking squares, we can see that this is a stylistic picture of the fully completed puzzle: There are five separate grids, as given by the colours, and four points of overlap between those grids. It looks like we are expected to get nine items (most likely letters), one from each grid and one from each intersection, and then arrange them in the given order for our next step.
Looking at the grids, we see a variation from the usual Bonza pattern: For each colour there are two different themes, rather than just one. After a bit of thinking about these themes, it can be seen that for each colour the two theme words can be chosen to differ by a single letter. (A good "in" for this observation is the top right grid, for which the terms are very constrained.) The themes and different letters are as follows:
This gives us five letters for the grids, and gets us a good way toward the solution; now we hope to extract some information from the places where the grids intersect. When we look at these intersections we see that there are clusters of squares with white backgrounds at those locations. (As opposed to the squares with white foreground, which were simply at the intersection of two colours.) Looking at these a little more closely, each cluster of white squares surrounds a group of black squares that are shaped like a letter of the alphabet. This gives us the remaining four letters that we need: U (top left), J (top right), M (bottom left), and A (bottom right).
Arranging the letters in the given order spells out EMUWARMAJ. Looking up the Emu War reveals that the major in command was Major G.P.W. Meredith of the Seventh Heavy Battery of the Royal Australian Artillery. This Australian link is also appropriate since "bonza" is a piece of Australian slang, meaning "great" or "terrific".
The solution is GPW MEREDITH. We also accepted MEREDITH.