I have a battery case for my Android phone and recently, the Micro USB connector that recharges it broke off. Since the warranty expired, I decided to open up the case myself and take a look inside. It seems that the connector is soldered to the board with four connections. I have some soldering experience, but never with components this small. Is it possible to solder the connector back in place and if so, do you have any tips on how to accomplish this and what tools I would need? Thanks.

Here is an album of images: http://imgur.com/a/2YL5z

 

Go on Youtube and type in the search field...
"how to solder micro electronic components"
Its gonna take a special tool for what you want to do....
There are a number of great videos...
hope that helps...

 

looking at the connector it looks like a few pins have broken off and may still be soldered in place on the pcb but the couple of pins remaining on the connector have part of the pcb track still connected so unless you have the correct tools to hand the pcb itself is scrap as far as refitting that connector is concerned.you are dealing with a double sided plated thro pcb-some phones use multilayer pcbs so without the correct rework station a replacement pcb /phone is required

 

you will need some hot air soldering rework stations for that.. since its that small.. like dthx said, look through youtube, you'll find some sorts of techniques there..