Is it found in the scriptures this statment “It is necessary to take a copy of your Family History records as you pass through the veil into eternity?”
No, that quote is not found anywhere in the scriptures. I think you’ll be hard pressed to find that quote anywhere outside the scriptures. There is an underlying principle that I think is getting hinted at with your statement.
When the prophet Joseph Smith first taught the principle of baptism for the dead, the saints were so excited to perform the ordinance for their ancestors that they baptized right away in the Mississippi River. While pondering on the principle further, the prophet received clarifying revelation. He wrote D&C 128 describing the importance of recording the ordinance. The saints in Joseph’s time learned that the baptisms they performed would have to be done again, in the proper order. Take some time to read this section and understand it and you’ll see why our temple records are so important.
The reason we keep family history records is so we can identify our dead ancestors who need the saving ordinances. This information is only a preliminary step but is not eternally significant. The really important record is the one that states that a baptism has been performed, that the other saving ordinances are completed, and that there is a sealing chain all the way back to Adam. The priesthood keys given to Joseph Smith empowers us to keep these records, and in recording it here it is recorded in heaven (128:8). Ultimately the dead will be judged out of these books (128:6-7).
Undoubtedly your ancestors appreciate the work you have done to identify them. As you take their names to the temple, the work is recorded both in earth and in heaven. The temple will have a record of the family chain, as will the book of life. If you follow the proper protocols and take care of the paperwork on earth, you don’t need to worry about carrying an extra book through the veil as a similar book is on the other side.