Of course there may well be similarities between the early Christian church and current day Mormonism. However, as a Christian and an ex-Mormon, I would deny that there are any uniquely Mormon activities today that were performed in the early Christian church - where those activities were orthodox and not apostate.
We know of the apostate teachings of some early Christians regarding baptism for the dead - found in 1 Corinthians 15:29. Paul argued against them. If this is the early teaching that your LDS friend is talking about, then he is correct. In this instance some of the early church did perform activities that the current LDS church also performs.
Understand that the LDS church is constantly seeking for support for their belief - whether that be in early writings or in South American archaeology. Just let them search - its all in vain.
One of the earlier posters talked about the Early Church Fathers. They are so very definitely Catholic. Yes, some LDS will say that the church was apostate by then. One article that I read said this (a slight paraphrase): “in the mid first or second century, the lights went out so to speak, and when they came back on a century or so later, all the chairs had been rearranged”. This was a reference to the apostasy of the early Christian church. Mmmm… interesting logic here.
I heard Father Pacwa say that trying to understand LDS doctrine is like trying to grasp hold of mercury (the metal). i.e. impossible. LDS doctrine changes depending on the prophet in charge. Christ is the Bridegroom, the Church is His Bride. Did the Son of God abandon His Bride for 1500 or so years as the LDS believe? Did He in retribution for the death of His Son take His authority from the Church until in the 1800’s He restored it through Joseph Smith. That was some “time-out”!! Did we learn our lesson by the 1820’s? It is in this area that I feel it is most fruitful to have LDS people start to think and ponder. Plant those seeds at the very heart of their beliefs - because everything hinges on their “Great Apostasy”.
Look today at who speaks to the World for Christianity: Pope Francis or President Thomas S. Monson? Who raised their voice against the bloodshed in Syria, or the horrors of human trafficking? Even when Mormon missionaries come to your door, what are they preaching? Christ? Nope. The Restoration and Joseph Smith, thinly veiled with Christ. It is more about getting people into the LDS church than it is in getting them to Christ. Sit in a Mormon sacrament meeting or their priesthood or Sunday School. Christ is their - vaguely. But the emphasis is in keeping the members LDS.
Love and Charity always. Reason and faith.
Peace be with you.
Prince Hal.