The mechanism of action of APF is via following reaction products:
When APF is applied on the teeth, it initially leads to dehydration and shrinkage in the volume of hydroxypatite crystals which further on hydrolysis forms an intermediate product called dicalcium phosphate dihydrate (DCPD). This DCPD is highly reactive with fluoride ion and starts forming immediately when APF is applied.
Fluoride penetrates into the crystals more deeply through the openings produced by shrinkage and leads to formation of fluorapatite.
For the conversion of whole of DCPD so formed into fluorapatite, deeper penetration and continuous supply of fluoride is required. Because of this reason, APF is applied every  30 seconds and the teeth has to be kept wet for 4 minutes. 
Because high fluoride concentration and low pH favor fluoride deposition, acidification of the fluoride solution with phosphoric acid was found to suppress the dissolution of enamel, as well as the formation of calcium fluoride and provide a more effective treatment. 
The intermediate product formed is the dicalcium phosphate dihydrate and calcium fluoride is the principal reaction product.

​Essentials of preventive and community dentistry 
Soben Peter 
5th edition
Fluoridated hydroxyapatite
Stannous trifluorophosphate
Dicalcium phosphate dihydrate (DCPD)
DCPD + Calcium fluoride + fluorapatite