James Burgess’ notes for Joseph’s May 21, 1843 discourse contain the following summary:

There are three grand Keys to unlock the whole subject. First what is the knowledge of God, Second what is it to make our calling and election sure. Third and last is how to make our calling and election sure. Answer, it is to obtain a promise from God for myself that I shall have Eternal life. that is the more sure word of prophycy… to be sealed with the Holy Spirit of promise, that is the testimony of Jesus.

-Joseph Smith, May 21 1843, James Burgess Notebook

Joseph made many statements about the importance of “the testimony of Jesus.”  He pointed out that Revelation 19:10 says that “the testimony of Jesus” is “the spirit of prophecy”, and possessing it made one a prophet.  The summary quoted above should clue us in to the fact that “the testimony of Jesus” is more than just “having a testimony” in the sense Latter-day Saints use it.  A friend wanted to know my thoughts on the connection between the testimony of Jesus and being sealed with the Holy Spirit of promise.  I wrote back:

In Joseph’s 1839 John 14 discourse, he describes the Savior’s work as the second comforter. He comes to you, cleanses you, and seals you up to eternal life.

[verse 16] I will pray the father & he shall send you another Comforter. There is one Comforter [Holy Ghost] & another Comforter to abide with you forever, reach to things within the vail, know that you are Sealed. If you get it, it will stand by you forever. How is it obtained? Keep my commandments & I will pray &c.—
[verse 17] It is a privilege to view the Son of Man himself, he dwelleth with you & shall be in you, his spirit shall be in you. [verse 18] I will not have you comfortless, I will come to you, abide with you forever, Seal you up to Eternal life.

It seems clear to me that “the testimony of Jesus” means “Jesus’ testimony.” But His testimony of what? When he comes he bears testimony about himself, and he bears testimony about the person to whom he comes. We can read many instances of Christ testifying of himself when he visits people (3 Nephi 11, Ether 3, D&C 93:1-2). We can also read instances of him testifying of an individual’s acceptance and future exaltation (D&C 132:49-50, LoF 6:7-8, JST Gen 14:27, Hebrews 11:4-5, etc). Christ bears that testimony to the individual to be accepted and to the Father, and that testimony is an essential component of his ministry as the Second Comforter. (D&C 88:74-75). In Joseph’s writings and recorded teachings, you find that these two testimonies (of himself, and of the acceptance of the recipient) are inseparably linked. Thus, it is hard to separate “the knowledge of God,” “making your calling and election sure”, “the testimony of Jesus”, “the other [or second] comforter” and “being sealed by the holy spirit of promise” when you are reading Joseph’s words. He linked them all, and when he is speaking of one, the others are apparently assumed to be present also.