In my experience, it is pretty close to impossible to get a company-financed relocation if you are doing the exact same job - it doesn't make financial sense for them. I've seen companies pay for a relocation for someone who is moving to a different role, even if it is a lateral move.
I would, therefore, expect that you'd be paying your own relocation costs.
I did this once. I told my boss that my family had decided to move to X city for personal reasons. I would love to continue working for the company, but I'd have to do so remotely. I cited an example of someone else who had done something similar. If they were unable to accommodate that request, I'd be submitting my resignation effective X date several months from then. They went along with it...but I was fully prepared to quit and they knew it. If you don't want to make that commitment, then you could just tell the boss that you'd be starting to look for other opportunities within and outside the company. This is risky.
In your case, my justification would focus on costs and potential benefits. If they are going to lose money on this, they'll probably say no.
a) particulars about the office you plan to work in - especially about office space. If they have to find you another desk that isn't already assigned to your group, then that's usually a charge to their cost center
b) What would change about your work? Is the time zone the same? Are the working hours the same at the other site as at yours?
c) how much additional travel would you have to do? How much would that cost the company?
d) are there things about your role that you cannot do in the new location? Are there things you could add to your responsibilities at the new location (new user base?)
I would also cite examples of others who had done similar things in the past...successfully!
Good luck!