The court records conclusively show that Porter stated his authority as a whole came directly from Lincoln, so in that since he did indeed give it his blessing. The court records also conclusively show that Lincoln personally intervened to prevent the contempt order from being served upon Porter, which demonstrates specific sanction for Merrick's house arrest by Lincoln.
And the difference between authorizing and ordering is what?
If I were president of your homeowner's association and I give you a paper stating "you are hereby directed to collect five dollars in annual dues from every person living on Oak Street" it would be an order.
If you came to me and said "Jim Smith on the corner of Oak and Elm hasn't paid his dues and has an old toilet that he's using as a flower planter in his front yard. May I fine him" and I said yes, it would be an authorization.
In Murphy's case, Porter appears to have gone to Lincoln and said "you know, Abe, I've got all these judges jumping on my back and being nuisances to what we want to accomplish. Can I do something about them?" and Abe said yeah, thus making it an authorization.
If you're saying Lincoln authorized it because he suspended habeas corpus then that's another.
No. He authorized it for this specific case by giving sanction and cover to Porter, most notably in his intervention to block the contempt order from being served.
Porter claimed that his authority came from President Lincoln when he refused to allow the writ to be served. And in a way he was correct since the order suspending habeas corpus was issued by President Lincoln. But where does Porter say that he was detaining Merrick specifically on the order of President Lincoln?
No. He authorized it for this specific case by giving sanction and cover to Porter, most notably in his intervention to block the contempt order from being served.
But where did Lincoln specifically order the detention of Merrick, like he is supposed to have specifically ordered the detention of Taney?