This page disagrees with you. Can you explain why?

http://www.splung.com/content/sid/2/page/momentum

Look at the "explosion" animation at the bottom of the page. It violates your "law of conservation of magnitude of momentum".

The collision animation above it can be made to violate your law too. Change mB from 1kg to 3kg, then press play. The total momentum before is 1kg*2m/s = 2Ns. The sum of the magnitudes of momentum after is 1*1 + 3*1 = 4.