If it's clear from context that the user suggesting the edit is the same person as the user who posted the post, then yes, please do approve the edit. Typical clues include:
- The poster is an unregistered user (identified by a browser cookie rather than a long-term credential), who is rather new to Stack Exchange (typically, that's their first question).
- The suggested edit is either anonymous or from an account created later than the post. If the latter, the account has the same display name and avatar, or has manually chosen display name and avatar as opposed to userNNN and the Gravatar hash patterns.
- The edit adds information that was requested and is not controversial in any way.
- The wording of the edit suggests that this is the same person (“here's my configuration as requested”, as opposed to “I have this problem too”).
While it's theoretically possible that someone would suggest such an edit with incorrect information because they have the same problem or just to troll, it's unlikely. “I have the same problem” cases are clear from wording. Troll cases can happen, but on factual matters, there's nothing to troll. If an edit suggests text that's an opinion piece, then you should reject it.
Accepting the edit obviously helps the original user. It also helps the site as a whole it means that the post will get into an acceptable state sooner, so there are fewer moderation actions to take, there are fewer bad posts around, and helping the user drives engagement up.
If the suggested edit is from a second account, please leave a comment pointing to the help center, something like
You seem to have accidentally created a second account. Please see [the help center](https://android.stackexchange.com/help/merging-accounts) for how to merge them. Once you merge your accounts, you will be able to edit your posts directly.
This is the policy I follow (whether I'm a moderator or not, I don't see why it would make a difference), and until I saw your question in the moderator election it wouldn't have occurred to me that a site would have a policy against it. Having now seen this meta thread, it still isn't clear to me:
I'm not a regular here and I don't have enough reputation to review suggested edits, so don't worry, I won't approve edits by a second account of the same user on this site. Nonetheless I'd like to understand why you find my behavior (on other sites) objectionable.