In textbooks people claim that conversion of ADP to ATP as the biosynthesis of ATP using ATP synthase. IMHO, it is NOT ATP synthesis! It is just a phosphorylation reaction carried out by ATP synthase.

"The redox regulation of ATP synthesis is accomplished by a cooperative interaction between two γ subunit domains of CF o CF 1 unique to photosynthetic organisms," says Prof. Hisabori.

Protons passing through F O (the pore) cause the γ stalk to rotate, inducing conformational transitions in the β subunit that are required for the synthesis of ATP from ADP. 9,10 The synthesis ...

Here, the dehydration synthesis of ATP which began with the reduction of oxygen to water by complex IV is completed, by the addition of a phosphate group to ADP to form ATP.

The new findings appeared June 3 in the journal Science, in an article entitled, “ADP-Ribose–Derived Nuclear ATP Synthesis by NUDIX5 Is Required for Chromatin Remodeling.” ...