UPDATE:
I have got a call with the VMware Product Marketing, VMware Support Manager and the TSE himself.
Here a Summary of that call... (original text from VMware Support Engineer).
Issue: Migration of Custom Attributes from vSphere Client with Migration Wizzart into Web Client is not working.
Following our internal investigation this is an engineering bug in the code of application.
Unfortunately at this point issue will be resolved in vSphere 5.1 Update 2 that is being schedule to be release at Q4/2013 or Q1/2014.
There is no valid workaround, as it would require to make changes on the Inventory Service DB ad code and WebClient code as well.
There is already engineering bug open and your ticket is assign to it. When resolution will be available, you will get additional email from VMware Support with further instructions.
So, in my case, I haven´t any workaround.
What we can do:
1) Keep the old vSphere Client
OR
2) Migrate the Custom Attributes manually
I know, it´s a hard work to migrate it manually, and it is very frustrating that VMware cannot solve this at the moment.
YOU ARE NOT ALONE!!!
It was a big mistake from VMware for all the enterprise customers.
And 1 jear of transpose time is for us tooooooo MUCH!!
VMware: SOLVE THIS BUG ASAP!
I will give all for us to get an valid solution!!!!
I will keep you up-to-date...!
Thanks, Jo!