Upgrading DRAM in one Computer and re-using the old DRAM

I have two laptops. One has 2 x 4GB 1600, 1RX8, 4G, DDR3L, S. It can take 2 x 8GB DDR3L SoDIMMs, therefore I plan to upgrade this one the 2 x 8GB.

My plan is then to use the 2 x 4 GB 1600 DDR3L and put them into another computer which can take 2 x 4GB but only has 2 x 2GB 1333 DDR3.

Would there be any problems doing this?