Having looked at the picture you sent, I agree with JEDLIPS your convergence amplifier if about to go bad. The reason the picture was necessary was to make a visual ID of the problem, TV's are very complex systems and to make snap judgments often leads to a misdiagnosis of the problem. However, since this is a convergence amplifier problem the credit for its diagnosis should go to JEDLIPS. There are many reference about this type of problem, here is one such solution just to get you started, but I would prefer that JEDLIPS gets the credit for diagnosis
Here is some advice I posted sometime ago, it applies in your case:
.This denotes a convergence problem as you surmised. Believe it or not it would be cheaper for you to replace the two convergence amplifiers and the biasing resistors. You would not actually be replacing the convergence board since these devices are usually located on the deflection board in most cases. However in answer to your question, the boards are easily removed, depending on your level of patience (lots of cables to move around), I would also advise you to either mark down all of the connection you will remove, or take pictures
of the board and its connectors. If you choose to just replace the Amplifiers and the biasing resistors there is a lot of information on this site on how to do so: This will get you started:
1) Unplug the TV and then get a schematic of the TV
I use http://www.servicemanuals.net or http://www.manualsparadise.com
2) On the schematic locate the STK392-xxx series IC packs (usually attached to a large heat sink)
3) determine if the STK392s are 110, 120 or 150.
4) if the STK392-xxx's are 110s replace with 110s (forget that upgrade stuff it is a hit or miss game
that I don't believe you want to get into), if they are 120s replace with 120s and so on.
5)Now to replace the STKs: remove the module from the TV and unsolder theold STKs along with the bias resistors, and replace them with the newones (be sure to apply heat sink paste to the STKs when attaching themto the heatsink
6) make sure there are no short circuits form your soldering job.
7) Reinstall the module and then turn on the TV.
8) do manual adjustment and the auto-convergence test and then things should be back to normal.
I hope this helps
Now if you think you can do this have at it, if not I would suggest that you have it done by a qualified TV technician.