I have now completely reinstalled my game and Origin and now the billing information works on the mailbox. After that, I added back my few mods piece by piece and restarted the game in between to test if the billing information at the mailbox still works. Everything was ok. Then I added back the last script mod and tested again, and lo and behold, the invoice information didn't open anymore. I then took this script mod out, restarted the game and it worked again. This is the script mod of TwistedMexi "TwistedMexi_T.O.O.L_sript". If you don't know it, you can use this mod to place objects off the grid. I guess that there were still some old data leftovers in the game, although I took everything out in the beginning. But now I was able to find out the reason after a complete reinstallation. It is definitely the TwistedMexi_TOOL_sript mod and not any of LittleMsSam's mods.
I will inform TwistedMexi on his Discord.