To answer a question.....Yes, the speaker wires run from the amp to the speakers.
The head unit is like the brains of the stereo system.....It tells the amp what to do.....If you take out the Becker head unit you will see that the lines out left and right, are on a yellow plug on top. The big difference between Becker and I think all aftermarket head units is that aftermarket units have DIN cables for their output, Becker uses wires. Why they did this I have no idea, its totally different. This is why I said that you'd be better off running the speaker wire straight to your head unit, I should have told you about the line out issue, I'm sorry I didn't mention it before. The other option I can see is to get yourself an aftermarket amp and keep the new head unit, or pull the speaker wires off the existing amp and run them to your new head unit. One more option just popped into my head as well......Splice the end of the DIN output cables on your new head unit, and attach them to the existing output wires which were on your Becker(the ones leading from the yellow clip). Just cut those wires making sure to tag them L and R, and you may be alright with that......These things can be a headache, because Beckers just aren't aftermarket friendly in their design....
Good luck!