Incorrect. There is a small portion in his son's handwriting, which is when Grant dictated to his son and his son wrote down what he said. Noble Dawson was a stenographer who also took some dictation from Grant. We have notes to Frederick in Grant's handwriting detailing edits to correct the text.
"The handwritten draft manuscript of the memoir, comprising more than 1,000 pages, is online in its entirety, revealing Grant’s edits and notes inserted by his son Frederick."
https://www.loc.gov/item/prn-17-148/papers-of-ulysses-s-grant-now-online/2017-10-10/
Bruce Catton: "All in all, Grant emerges as a man of letters of real distinction. Go back, again, to his performance in the Memoirs . He wrote this book against pain and death, and he stuck to it as long as he could hold a pencil—not because someone else could not finish the thing for him, thereby assuring his family a proper estate, but simply because as a writing man he wanted the book done his way. No professional author could have written a sturdier declaration of dedication to his craft: 'I do not want a book bearing my name to go before the world which I did not write to such an extent as to be fully entitled to the credit of authorship.' "
https://www.americanheritage.com/us-grant-man-letters
"Though illness continued to interrupt his work, Grant could tell Clemens on May 26 that he had made the book too long by 200 pages. As proofs were received they were read to him; he made revisions, either dictating or writing them. By early June a great part of the Wilderness and Appomattox sections were set in galleys. A prospectus for the book, containing material from the early years to Appomattox, was given to the canvassers on June 8. Grant's son Frederick now acted as chief researcher, checking facts and finding particular letters and dispatches written during the war. Grant's other sons, Ulysses Jr., and Jesse, also helped. This pattern of work continued even after Grant left New York on June 16 to spend the summer at Mount McGregor, New York. The Webster stenographer, Noble E. Dawson, accompanied the family and not only took dictation but helped Frederick Grant in copying and inserting new additions and revisions into the proofs. There were very few days now when Grant could dictate to the stenographer because the cancer in his throat made speaking too painful; instead, using a pencil and a special lap table, he wrote out his new sections and made notes for revisions. Clemens came to Mount McGregor the evening of June 29 and stayed until July 2, during which time Grant wrote the Preface. The first volume was completely set in type, but Grant continued to make last-minute revisions and notes for it until the first week of July. He was also organizing and rewriting the second volume. He was pleased with his revisions of the Appomattox section but felt that he did not have the time to revise the other sections. At one point in a note to his son Frederick, he wrote: 'I should change Sptts. if I was able and could improve N. Ana and Cold Harbor.' He also went over the contents of the Appendix with Frederick. The last two chapters were written at Mount McGregor. By July 10, all of Volume I was in page proofs and ready for the press, and by July 18, the text of Volume II was copied and ready for the printers, except for the documents that sitll had to be inserted, both in the work itself and in the Appendix. Grant died at Mount McGregor on July 23, 1885." [Mary Drake McFeely and William S. McFeely, eds.,
Personal Memoirs of U. S. Grant, Library of America edition, pp. 1165-1166]
We've been on this merry-go-round before. The claim Grant didn't write any portion of his memoirs is complete and utter bull.