Sewing fake leather on top of synthetic fabric

Hello, I am a noob when it comes to sewing. So now i want to sew a fake leather on top of a synthetic fabric. See picture. The problem is that, especially, on larger sizes (like 1 meter) bubbles/foldings start to appear. I tried needles and even the stapler to prevent this for happening. No luck so far. It seems that the fake leather has more stretch and the synthetic fabric. What the way to go? I use a Singer 1480, straight stitch.
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