This may or may not be helpful. I believe Liverpool Solomon Hart is my 2nd great grandfather. According to 23andMe I share a 3rd great grandparent with the person I can trace to Rachel Haring. That would suggest our link is with that Rachel’s mother Mietje but not further back. It may be possible that that Liverpool Solomon Hart and Rachel Haring are cousins, but then we would not be linked by my 3rd great grandparents (perhaps 4th). Of course, it is quite 23andMe’s estimate may be out by one generation.
With regard to your note: “Liverpool Solomon's mother seems to be Salomon Alexander Haring's younger sister, Mietje (Maria 1792 - 1818). I think her death triggered her husband Salomon Offenbach to take Liverpool Solomon and his sister Chana (Hannah) to Glasgow.”
The names get confusing so I will only use those that occur on the Geni tree I linked previously. I think you are proposing that Liverpool Solomon’s mother and father are Mieje Alexander Haring (1792 -1818) and Hartog Solomon (Shlomo Swart Offenbach) (1784-d.). The Geni tree shows only one child of that marriage—Judic Hartog Stuart (1816-1817). The dates may be out but somewhere I have seen 1819 as the birth date of Liverpool Solomon. Is the death of Liverpool Solomon’s mother related to his birth?
In what year did Salomon Offenbach go to Glasgow?
I cannot see on the Geni tree Salomon Offenbach having a child named Chana (Liverpool Solomon’s possible sister). Where did you find information about Chana?