Just as Andre said. And env1ro has right as well regarding the order. Because the opposite way you might get trouble with some things.
Thank you all for your help. Now I know it exactly!
Sometimes the following method works:
1. Copy content from InDesign to Photoshop —> 2. Place it as smart object —> 3. Double click the smart object to launch it in Illustrator —> 4. Now fix issues if there are some (e.g. text layers) —> 5. Export as PSD including editable (text-)layers