Using DB is of course required for any link between two cubes. Having said that, depending on your version of TM1, if performance modeller is available, creating graphical links is probably the easiest way to get the job done. It creates the rules in the respective cubes rule files so it is also a good learning tool.
To the essence of your question, as a high level view, let's assume that TM1 calculates the cube by running through its cells. Each cell is defined by members for all dimensions specified. When you rule something, the !Date1 variable (i.e. ! in front of the Date1 dimension name) gives you the member for the Date1 dimension of the current cell. Therefore, given that your Cost/Profit Centre dimension is the same, shared across cubes (not optimal and it should probably be Account) you can map one leaf element to the other (!Account).
For dimensions that you have in the source cube, but not in the target, you have to create a total element to use in the DB.
Finally, whatever rule you create to pull data in your Finance cube, you also have to create a feeder in your respective source cube.