well, that power supply in your link is rated at 5V and you said that the iphone calls for 3.4... on the sticker at the link i see there is an option for a 3.7V unit - is such a unit available?

I do not know if the iphone can be powered by a 5V power supply but if the supplied voltage is greater then the system can take, it will burn the phone... The USB computer port supplies 5V DC at 0.5 A maximum, and since the iphone can be charged by the USB cable without any additional circuitry inside that cable, I would say that a 5V DC power supply should be sufficent...

What happens in those electronics, they need power supply that is a bit greater than the voltage of the battery, so the battery can charge... the battery voltage varies depending on the load and the state of the charge, from 3V to 4.5V and the phone has internal power regulator that will regulate the voltage applied to the chip, but the input voltage for the internal regulator inside the phone is within smaller brackets (say, 3 to 7 V DC), as bigger voltage brackets call for more heat dissipation... Now, the other issue is, if the power supply is capable of holding the 5V steady while the phone is "drinking" the amperage - if the power demand of the phone is great, the amperage draw is high, and the 5V can not be sustained, and the voltage drops below 5 V nominal, and at one point drops below the battery level threshold, at which point the charger stops charging... That is my problem, therefore I am looking for a more powerful charger that will hold the 5V steady while supplying higher amperage...

supposedly, a GSM standard calls for no more than a 2.5A of internal power consumption (which may or may not include the smart phone functions!). A 3A power supply proved to be insufficient, so I bought components to built an 8A power supply, which should hold 5V steady at 4-5A draw... we'll see how that thing comes along...

to be honest, i would not pay $8 for something that could be had for $3

Waterproof DC DC DC Converter 12V Step Down to 5V 3A 15W Power Supply Module | eBay

another thing - this unit in your link is a direct wire, meaning that you will need to source an iphone power cable/iphone connector and wire it up...

you may want to consider a USB variant of the same power supply, and just get a USB to iphone cable that is sold everywhere...

DC Power Converter 12V Step Down to 5V 3A 15W Power Supply Module with USB AF | eBay