Would God listen to the prayer of someone else on a person's behalf more, or would it be the same as if the person prayed for themselves?

The Bible encourages us to offer prayers in behalf of others. The disciple James even wrote: "Pray for one another." - James 5:16.

The apostle Paul set a good example of this:

"To that very end indeed we always pray for YOU, that our God may count YOU worthy of [his] calling and perform completely all he pleases of goodness and the work of faith with power." - 2 Thess. 1:11

But the question is: "Would God listen to the prayer of someone else on a person's behalf more, or would it be the same as if the person prayed for themselves?"

Psalm 65:2 tells us that Jehovah is the "Hearer of prayer" and from the Scriptures above, we can be sure that he listens when prayers of those wholeheartedly devoted to Him pray for one another. Jehovah hears "the prayer of the righteous ones." - Proverbs 15:29. (See: The Bible's Viewpoint - Prayers That Are Heard by God)

So there are some questions that need to be asked about the person praying on behalf of another:

Are they "righteous" in God's eyes? Do they really know who they are praying to? Do they incorrectly believe that God is a Trinity? Do they incorrectly believe that Jesus is God instead of his Father? Do they incorrectly believe that God inhumanely allows eternal torment for unbelievers? Do they even know that God's name is (Jehovah)? And on and on. (See: What could make a person's prayers unacceptable to God?)

Which prayer would Jehovah logically be more receptive to: The one who really knows who God is and who has a personal relationship with, or the one who is praying for the "righteous" one but doesn't even know who they are praying to?

For more, see:
Prayer - Links to Information (Search For Bible Truths)