There is nothing wrong with "someone else's". Inexplicably, many spelling checkers don't automatically recognize possessives of user-added words, so don't try to read much out of that.
From a grammatical perspective, the key insight is that -'s is not a word clitic, it is a phrase clitic. For example, it may be informal or even a little unidiomatic, but it is not ungrammatical to utter or write sentences like the following:
I take exception to the senator from Maryland's remarks.
The package that arrived on Monday's return address was somewhere in Texas.
The man I was talking to's attitude really bothered me.
Worrying about the placement of the possessive clitic is someone else's hang-up.