The precise language of the will is critical.Julius Allen senr dated his will in 1777.At that time Elizabeth Sharpe had been a widow and single mother since 1768. (William Sharpe's will was lost and its terms reported in a deposition by Susanna Storrs, a witness, in the proceedings related to records destroyed by the British.The order book for 1767-69, at p 210, states that at the April Court 1768, the will of William Sharpe was presented by Elizabeth Sharpe and William Sharpe, executors.)
That being the case, if Julius described the Elizabeth in his will as "my daughter" he could mean (in the usage of the time) either his natural daughter or daughter-in-law.The initial "M" may suggest the latter, as middle names were not typically used in the middle 1700s.She likely would have been born in the 1750s.
Even more critical is whether, in 1777, Julius refers to his daughter by given name only, or by the full name Elizabeth M. Allen (which the abstract indicates).It is most unlikely that he would refer to her as "Allen" if she were the widow "Sharpe" (and had been for 8 years or more).
What explanations are there for the initial "M"?If his natural daughter, is it a clue as to the identity of the wife of Julius senr, or his mother, or his wife's mother?Martin?Matthews? Mallett? Did Julius senr have a sister who married George Martin about 1742?
Looking at the dates of children and namings, perhaps Elizabeth Sharpe was the sister of Julius Allen senr.What is known of the children of Edmond Allen?