Cardio and strength training do work together.
The thong is, we don’t want to do strength training first thing in the morning, because we need bigger amount of energy for weight lifting (that we’ll get from the breakfast and lunch).
Cardio requires a smaller amount of energy, so it’s healthy to do it even on a empty stomach.
Now, when we decide to do a full body strength training and cardio training, we should always do weight lifting first, so that we avoid wasting our energy on cardio first.
So the choice is yours, do it in the morning or in right after strength training, eater way you’re doing the right thing :)