1) You can certainly do it "the long way," by first buying and activating the Moment on your mother's line, then switching your mother back to her old phone and activating the Moment on your own line.
2) If you order from Sprint's web site, and specify not to activate the Moment automatically, you may be able to shortcut the procedure by directly activating the Moment on your own line when it arrives. I did this successfully for my nephew last year. If Sprint complains or tries to goof up your account (which is highly unlikely), you can just say honestly that you were trying to save all sides the trouble of the longer procedure (1).
If you're dealing with rebates, this procedure (2) might goof up the rebate. But right now, Sprint's web site is offering instant discounts instead of rebates anyway.
3) There is no issue of "fraud" at all. Even in procedure (2), Sprint correctly renews the contract on the upgraded line, and marks it as recently upgraded. Procedure (2) really is just a shortcut of procedure (1).