You're making a simple mistake somewhere.  Check your work.

DjangoJay Converse AcumenTeam, could you help me what the mistake hides a link to the payment inside the invoice?

You were using the wrong endpoint.

cdn.na.sage.com/.../Sage300_WebAPI_EndpointReference.pdf

I don't see the related payment within the invoice on UI.

Then you're looking at the wrong UI.

The "Payment Received" and "Amount Due" fields on the AR Invoice only include "Prepayments" (either from AR or OE).

If a standard AR Receipt is entered and applied against an Invoice, the receipt amount is not reflected in the "Payment Received" or "Amount Due" fields on the AR Invoice (ARDINVO.rpt).