Also if Tax Invoice is in the name along with business address of Mr A , then A can account asset in the books of A even if payment is made by third party . it's libility of A to pay back to Third party .
In all this answer, it is possible if the invoice is in name of Mr. A but if it in name of third party, then ask the third party to raise invoice in name of mr. A with all taxes as this may be raised in audit with reference to related party a/c and also Gst rule issue.
Yes Of invoice is made in the name of A and if invoice is made in the name of third party then you cant directly for that third party permission required so show that transactions in third party books also