Answer
The answer is as follows. 
Katrielle and the Millionaires' Conspiracy walkthrough
Puzzle Location: The Treasury (The decanter on the table)
Place one jewel in each of the empty spaces in the jewellery box.
In the five-by-five grid, place the jewels so that there is one of each different kind in the horizontal and vertical rows.
Slide the jewels to move them where you want them to be inside the jewellery box.
The jewels in there originally cannot be moved.
Focus on the places where horizontal and vertical lines cross.
Look at the two lines and see which jewels are missing from both.
First, let's look at the bottom horizontal line.
The jewels missing from this line are red and orange.
The right vertical line has a red jewel in it, so this means the right-hand slot on the bottom line has to be orange.
Continuing on from hint two...
Next, let's look at the right vertical line.
An orange jewel was added to this line, so that leaves us with blue and green.
There's already a blue in the top horizontal line, so the intersecting slot between the two lines has to be green.
Continuing on from hint three...
Now let's look at the top horizontal line.
A green jewel was added to this line, so that leaves us with red and orange.
The bottom slot in the left vertical line is red, which means that the intersecting slot between the two lines must be orange.
The answer is as follows.