From DLA to PIP in Care Home

My son is severely disabled and needs 24 hour care from myself and carers. He moved into a care home in 2013 and lost his mobility car. However, we were told by DWP decision maker that if he returned home at any point he would have the DLA re-instated as he qualified for the higher rate for both care and mobility. We continued to have yearly notifications of his entitlement, but no payments presumably because he lives in a care home. For the last 5 years I have had to buy a WAV myself to take him out to appointments or on visits to family. We have just moved over to PIP and was awarded Enhanced rate for both Care and Mobility and will have the Mobility paid until 2028. can anyone explain why he wasn't paid the mobility component on DLA. Nothing has changed on our side.
Many thanks.

Thank you for your quick reply. This has been very useful. He is funded by NHS continuing health. Thank you for the link.
Cynthia