And the angel of Jehovah appeared unto the woman, and said unto her, Behold now, thou art barren, and bearest not; but thou shalt conceive, and bear a son. (Judges 13:3, ASV)
In this story the messenger of Yahweh "appears" to the woman and tells her she is going to have a child, very similar to our story above with Abraham. In verses 4 and 5 the messenger gives instructions to the woman about the child.
Then the woman came and told her husband, saying, A man of God came unto me, and his countenance was like the countenance of the angel of God, very terrible; and I asked him not whence he was, neither told he me his name. (Judges 13:6, ASV)
The woman identifies this messenger as "the man of Elohim" and then says, literally from the Hebrew, "his appearance was like the appearance of the messenger of Elohim." She also notes that he did not give his name, an interesting parallel to our story above with Jacob. In verses 7 through 12 the woman explains the events to her husband Manoah who prays to Yahweh asking for "the man of Elohim" to return, and he does, appearing to the woman again. The woman goes to Manoah and tells him "the man" has returned and he goes to meet him.
And the angel of Jehovah said unto Manoah, Of all that I said unto the woman let her beware. (Judges 13:13, ASV)
Now "the man of Elohim" is identified as "the messenger of Yahweh," but in verse 16 it states that Manoah did not know this. In verses 14 through 16 the messenger instructs Manoah about his wife and Manoah invites the messenger for a meal, who refuses
And Manoah said unto the angel of Jehovah, What is thy name, that, when thy words come to pass, we may do thee honor? And the angel of Jehovah said unto him, Wherefore askest thou after my name, seeing it is wonderful? (Judges 13:17,18, ASV)
Just as Jacob asked for the "man's" name, so does Manoah, and just as the man refused to give it to Jacob, he refuses to give it to Manoah. In verses 19 through 21 Manoah makes an offering to Yahweh and at this point realizes that he has been speaking with "the messenger of Yahweh."
And Manoah said unto his wife, We shall surely die, because we have seen God. (Judges 13:22, ASV)
Now we are told that this "man" that has appeared to them is Elohim.
 The definite article is present in the Hebrew