If you have your customized lists in the SplashShopper Desktop, export your list from the old user in SplashShopper Desktop:
File menu > Export > SplashShopper vShop
Repeat for other lists that you need to transfer (you need to be in All view for each list).
Download the new SplashShopper 4.0 iOS app (if you have not already):
Then run the new iPhone app, and do a sync with the SplashShopper Desktop.
Then switch the user in the SplashShopper Desktop user menu to the new (properly working) device name.
Now import your vSH files, creating new lists. Then sync again.
If your data is in the old iOS app only, and you are able to run the old app, you can email the items to yourself to be imported into the new SplashShopper 4.0 iPhone app. Here's how:
1. Open your old SplashShopper 3.x iPhone app
2. Select the list you want to transfer, and stay in the All items view
3. Tap the "mail" icon near the top of the screen (by the search icon)
4. Enter your own email in the to field and email it to yourself
5. Open the email when you receive it and tap the "All items" link to import into the new SplashShopper
6. Repeat for other lists if needed
7. And then the new 4.0 iPhone app should have your lists.