How can electron transport from photosystem II to NADP + lead to the synthesis of ATP?

The concept here is the movement of the phosphates. NAD and ADP are base molecules which are formed by the cell and are in plentiful supply. They do not themselves change, it is the addition or subtraction of the phosphates that is the key here.
Light energy is used in the electron transport system to activate NADP molecules. In donating their phosphate to an ADP molecule to make it ATP, they convert the light energy to chemical energy and it is stored in the phosphate bond in the ADP to ATP molecule.
The bottom line is that NADP and ADP (occasionally AMP also) are not formed in photosynthesis; they are already there. It is the exchange of the phosphate to convert them to NAD and ATP that is the essence. Both NAD and ADP (or AMP) remain unchanged and can be used indefinitely in the process.
Think of it like this: You have a wallet, and in it is a 20$ bill, and you give it to your friend, who puts it in his wallet.The money represents the chemical energy stored in the ATP molecule; your wallet represents NAD molecules. It's now empty, but you can 'recharge' it by putting another $20 bill in it.
Your friend's wallet represents ADP. When he gets your 20$ bill, his wallet is now 'charged' with energy that he can spend in a store, which represents the cell. His wallet is also reusable, and he too can add another 20$ to it for more spending power.
The bottom line here is that it is the exchange of phosphates, energized by light and then converted to chemical bonds in ATP molecules (which the cell can 'spend' directly) that is the point. The base carrier molecules of NAD and ADP are not changed in this exchange chemically except for the transferring of the phosphate, full of chemical energy, from one carrier molecule to the other.
You and your friend have wallets, and taking money out or putting money in does not change the structure of the wallets, and they can be used again and again.
I hope I didn't confuse you with the analogy, but sometimes it's easier to see these things when you can visualize them in a different way.

At photosystem II the energy derived from absorption of photons is used to split water molecules to molecular oxygen and protons. This reaction takes place within the thylakoid lumen, so the release of protons from H2O establishes a proton gradient across the thylakoid membrane. The high-energy electrons derived from this process are transferred through a series of carriers to plastoquinone, a lipid-soluble carrier similar to coenzyme Q (ubiquinone) of mitochondria. Plastoquinone carries electrons from photosystem II to the cytochrome bf complex, within which electrons are transferred to plastocyanin and additional protons are pumped into the thylakoid lumen. Electron transport through photosystem II is thus coupled to establishment of a proton gradient, which drives the chemiosmotic synthesis of ATP.

From photosystem II, electrons are carried by plastocyanin (a peripheral membrane protein) to photosystem I, where the absorption of additional photons again generates high-energy electrons. Photosystem I, however, does not act as a proton pump; instead, it uses these high-energy electrons to reduce NADP+ to NADPH. The reaction center chlorophyll of photosystem I transfers its excited electrons through a series of carriers to ferrodoxin, a small protein on the stromal side of the thylakoid membrane. The enzyme NADP reductase then transfers electrons from ferrodoxin to NADP+, generating NADPH. The passage of electrons through photosystems I and II thus generates both ATP and NADPH, which are used by the Calvin cycle enzymes in the chloroplast stroma to convert CO2 to carbohydrates