I'm in a similar process of trying to change offices. In my situation, I have very personal reasons why I need to move closer to home, and I was confident that my partner/HR person would sign off on getting me switched out. Now, depending on your reasoning, I've heard mixed advice. Take what I say below with somewhat of a grain of salt, since I'm still in this process and my situation probably differs from yours.
The dilemma is that it's a bit of a catch-22 in that you're kind of putting yourself out there and will probably shoot yourself in the foot either way if it fails. If you reach out the the other office's HR first, your home office will not be a big fan of you and it could be seen as slightly underhanded. These are basically separate businesses operating under the same umbrella and partners don't like to see people they've trained leave. That said, if you tell your office's HR that you want to leave, you might get slightly screwed in that now the office knows you aren't going to be here and has no incentive to give you the opportunities you want till the time you transfer.
When I was deciding what to do, I decided to just go to HR at my office because, if HR/the partner wouldn't support me for my very real reason for leaving, then frankly, this firm doesn't care enough about me and I won't stay long anyway. Second, if I talk to them first, I figured the partner would be much more sympathetic toward signing off on the transfer than if I went to the other office and undercut them. However, I can also see how it's beneficial to have another office already clamoring for you, so if you think you can pull that off, go for it.
Just for general info, the basic process (if you go to your HR first) is that HR will talk to your office's head partner and explain the situation. If the partner signs off on it, then your HR person will connect you to the other office and begin discussions assessing the need of the other office, your fit, etc. After that, I'm not sure as I'm still finding out what's going on, but hopefully this helps a bit.
My best advice is really think about how legitimate your reason is for leaving and if your current situation is bad enough to make you want to leave the firm if necessary. My guess is that internal transfers are WAY easier than getting hired externally, but it is risky, IMO, because the firm will know you aren't sticking around and therefore be less likely to accommodate you while you're here.
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DONE!
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