irESA to UC migration - Do i notify ESA when migration is complete ?

Hi

I've just about completed the process of irESA to UC migration and it seems to have gone smoothly. I'm about 3 days away from what should be my first UC payment.

They've just posted a message on my journal saying:

Some benefits can affect how much Universal Credit you receive. Our records show that you are not getting any of these benefits.
Benefits that can affect Universal Credit are:
Jobseeker's Allowance
Employment and Support Allowance
Carer's Allowance
Carer Support Payment
Maternity Allowance
Bereavement Allowance (including Widowed Parent's Allowance)
Widow's Pension (including Widowed Mother's Allowance)
State Pension
Incapacity Benefit
Severe Disablement Allowance
Industrial Injuries Disablement Benefit
If you are actually getting one or more of these benefits, you must contact the office you claim them from. Tell them you're now getting Universal Credit and to update their records.

During my assessment period for UC migration i have continued to get payments but in my bank account they are shown as from DPW EESA and also GB CPS FP ACC.

Qusetion: Do i need to let ESA know when i complete migration into UC even for automatic irESA to UC migration situations ? I'm a bit confused.

Thanks for the advice.
twzzz