Among Muslims, the term "last command" of the Prophet Muhammad is usually referring to a sermon the prophet gave at his last Hajj, a few months before his death.

The prophet said upon his disciple to treat women well, to remind people that an Arab has no superiority over a non-Arab, nor does a non-Arab have any superiority over an Arab; white has no superiority over black, nor does a black have any superiority over white. He ask his disciples to keep the daily prayers and giving alms to the needy. And most decisively (theologically speaking) he iterated that there shall be no more prophets after him and that the religion of Islams is a complete faith.

There was no mention about command to conquer Constantinople, the then capital of the (Eastern) Roman Empire. There was however, an account of sort of prophecy as recorded in one particular hadith (collection about the prophet's saying) that one day Constantinople shall be conquered by Muslims army and, according to popular beliefs, the leader of that army is like him (namely his name shall be Muhammad). And lo and behold, in 1453, the city was conquered by Mehmed II of Ottoman Empire ("Mehmed" is Turkish version of the name Muhammad). Although this hadith is disputed as whether it is shahih (credible) or not, and whether he merely predicted that Constantinople will be conquered instead of Rome city (It's confusing really, more here)

Edit: see the hadith I referred in comment below by /u/son_gokuu_sjw3

"Lataftahanna al-Qustantiniyya wa lanima al-amiru amiruha wa lanima al-jayshu dhalika al-jaysh."

"Verily you shall conquer Constantinople. What a wonderful leader will her leader be, and what a wonderful army will that army be!"

Narrated from Bishr al-Khathami or al-Ghanawi by: Ahmad, al-Musnad 14:331 #18859 [sahih chain according to Hamza al-Zayn] al-Hakim, al-Mustadrak 4:421-422 [sahih according to him and al-Dhahabi concurred] al-Tabarani, al-Mujam al-Kabir 2:38 #1216 [sahih chain according to al-Haythami 6:218-219] al-Bukhari, al-Tarikh al-Kabir 2:81 and al-Saghir 1:306 Ibn Abd al-Barr, al-Istiab 8:170 [hasan chain according to him] al-Suyuti, al-Jami` al-Saghir [sahih according to him]

This could be a reference to verse 9:29 of the Qur'an, which was one of the last verses of the Qur'an to be revealed.

"Fight those who do not believe in Allah or in the Last Day and who do not consider unlawful what Allah and His Messenger have made unlawful and who do not adopt the religion of truth from those who were given the Scripture - [fight] until they give the jizyah willingly while they are humbled." (9:29, trans. Sahih International)

According to Tafsir Ibn Kathir, a classical commentary on the Qur'an, this verse was revealed regarding fighting the People of the Book (Jews and Christians) after the Arabian peninsula was conquered and the pagan Arabs defeated. This led directly to the Tabuk Expedition, which was the last military campaign of the Prophet Muhammad. He led the Muslim army to Tabuk with the intention of fighting the Romans, but they weren't there so no actual fighting took place.

Tafsir Ibn Kathir:

This honorable verse was revealed with the order to fight the People of the Book. After the pagans were defeated, the people entered Allah's religion in large numbers, and the Arabian Peninsula was secured under the Muslims' control. Allah commanded His Messenger to fight the People of the Scriptures, Jews and Christians, on the ninth year of Hijrah, and he prepared his army to fight the Romans and called the people to Jihad announcing his intent and destination. The Messenger sent his intent to various Arab areas around Al-Madinah to gather forces, and he collected an army of thirty thousand. Some people from Al-Madinah and some hypocrites, in and around it, lagged behind, for that year was a year of drought and intense heat. The Messenger of Allah marched, heading towards Ash-Sham to fight the Romans until he reached Tabuk, where he set camp for about twenty days next to its water resources. He then prayed to Allah for a decision and went back to Al-Madinah because it was a hard year and the people were weak, as we will mention, Allah willing.