How can I link battery life to resistivity of a phone PCB?
As you can see from the comments, the answer is conditional.

In most cases, in a modern piece of electronics, using a more conductive element in place of copper will reduce power losses across that trace. It is worth pointing out, though, that with the miniscule currents used in a typical mobile device, there shouldn't be any meaningful gain in battery life, especially not when compared to cost.

Heating power losses are linearly related to resistance, but are geometrically related to current flow. Silver only has about 5 percent better conductivity than copper, so, for the same amperage, could reduce those heating power losses by about 5 percent.

Keep in mind, though, that a mobile phone doesn't employ a fan - it has to dissipate all heat generated through it's case. So some very clever people already had to reduce those heating power losses to get it to work at all. They really are quite small in comparison to the amount of power consumed by the active electronics, especially a big, pretty touchscreen or a radio that passes high-speed data to a tower miles away - that's where all the power is going. A five percent reduction in heating power just from the pcb wouldn't be noticed.