Why Email-To-Case doesn't work anymore when my flow is active?

Hi all,

There is  the following scenario:

• Supposing there is an existing case created via Email-To-Case (a customer sent an email and this created a case via E2C)
• An agent forwards this email to the email address 'internal-team@gmail.com'
• The team member behind that email address responds the thread 
• The team member gets an auto-reply via Case auto-response rule

So, in order to prevent that auto-replies are sent to the email address 'internal-team@gmail.com' I created a custom field, say 'no-autoreply email address', type Text.

The flow should set the value of the FromAddress in the Email Message on the custom field on Case.

I am only mentioning 'internalteam...', but there are more than 40 email addresses where an auto-reply should be prevented.

Why I created this custom field on Case and why I would like it to be set automatically via flow? Because I want to use that field on the existing Case auto-response rule as an additional criteria.

What is the problem?: When my flow is active, E2C doesn't work anymore.

Can please somebody help me to understand what I am doing wrong?