This honorable Ayah contains a glorious ruling from Allah. Allah's statement,
{O you who believe! When death approaches any of you, and you make a bequest, then take the testimony of two...}

meaning that there should be two witnesses in such cases,
{just men...} thus, describing them as just,
{of your own folk} Muslims,
{or two others from outside} non-Muslims, meaning the People of the Book, according to Ibn 'Abbas as Ibn Abi Hatim recorded.
Allah said next,
{if you are traveling through the land} on a journey,
{and the calamity of death befalls you.}

These are two conditions that permit using non-Muslims from among the Dhimmis for witnesses when there are no Muslims present: When one is traveling and needs to write a will, as Sharih Al-Qadi said. Ibn Jarir recorded that Sharih said, "The witness of the Jews and Christians is not allowed except while traveling, and even then only to witness the dictation of the will." Allah's statement,
{Detain them both after the Salah (the prayer),}

refers to the 'Asr prayer, according to Al-'Awfi who reported it from Ibn 'Abbas. This is the same explanation reported from Sa'id bin Jubayr, Ibrahim An-Nakha'i, Qatadah, 'Ikrimah and Muhammad bin Sirin. As for Az-Zuhri, he said that they are detained after Muslim prayer (i.e., in congregation). Therefore, these two witnesses will be detained after a congregational prayer,
{let them both swear by Allah if you are in doubt.}

meaning, if you are in doubt that they might have committed treachery or theft, then they should swear by Allah,
{We wish not in this} in our vows, according to Muqatil bin Hayyan.
{for any worldly gain} of this soon to end life,
{even though he be our near relative.} meaning, if the beneficiary is our relative, we will not favor him, or favor anyone for his honor. This is discussed in the studies of the oaths in the books of Ahkam. Allah's statement,
{That should make it closer (to the fact) that their testimony would be in its true nature and shape (and thus accepted),}

means, the ruling requiring the two Dhimmi witnesses to swear, if there is a doubt that they were not truthful, might compel them to admit to the testimony in its true form. Allah's statement,
{or else they would fear that (other) oaths would be admitted after their oaths.}

means, requiring them to swear by Allah might encourage them to admit to the true testimony because they respect swearing by Allah and they glorify and revere Him. They also fear exposure if the heirs of the deceased are required to swear instead of them. In this case, the heirs would swear and earn the rightful inheritance that the two witnesses failed to declare. This is why Allah said,
{or else they would fear that (other) oaths would be admitted after their oaths.}