CF83 shortly before or after reaching pension age

Can you please confirm the position of a person who lives or lived abroad and who wants to fill gaps in their NI record but is within 6 months of reaching UK pension age, or has already claimed their UK state pension? Do they still send CF83 to HMRC to establish the years they can pay and the Class of NI they should pay, after which they speak to DWP Future Pension Centre or the Pension Service, to establish which years will improve their pension, or is the process different, as someone suggested to me recently? That person suggested they had been told by HMRC that they should not submit a CF83 but should simply contact the Pension Service.

Hi,
If you send us a CF83 application form to pay voluntary National Insurance contributions when you are close to or over UK State Pension Age, then it will be automatically forwarded to The Pension Service for them to process and reply to you.  
They will advise you of your current and future entitlement to a UK State Pension and detail any shortfalls of voluntary contributions that you may pay.  
If you prefer then you can contact The Pension Service direct and they will start the same process – their telephone number is:  +44 191 2187777 (from overseas).
I hope that this is OK.
Thank you.

Thank you but can you explain the rationale behind this, given that HMRC has responsibility for National Insurance and the requirements that need to be met to pay voluntarily at Class 3 as well as Class 2? What is it that differentiates between being "not close to" and being "close to or over", pension age? Is there a particular expertise in DWP, or do they still liaise with you on the National Insurance legislation? It just seems an unnecessary and potentially confusing syb-process.

Hi,
HMRC has limited access to your qualifying years for pension when you are close to, or over State Pension Age.
The International Pension Centre have full access, therefore they are responsible for quoting any shortfalls when you are within 6 months of, or over State Pension Age.
They are fully trained in assessing your request and quoting the correct rate of voluntary National Insurance contributions that are applicable to you (class 2 or class 3).  
Thank you.