These aren't the easiest things to research, so well done for getting this far. I'd agree with most of your transcript, except that I think the Executor is Thos WAILES, and the Folio is 1879.
I think (but am not 100% certain) that the Succ. Ledg. is a reference to a later entry - cf the bottom entry on that page, which has a number in that column. If so, the "tick" may actually mean there's nothing entered there.
The Ledger column appears to be blank - the "21" stamped at the top is a folio number relating to the whole sheet.
The IR27 documents are an index to the actual Death Duty Registers, which are held by TNA in class IR26. If you go to the TNA catalogue and enter reference IR26 for the year 1822 you get 64 results, and it's possible, by process of elimination, to work out which of these contains the entry you want. What you need to find is an entry with the correct initial letter of the surname at top left, and in the second line of description, a range of folio numbers corresponding to the one you have from IR27 - 1879.
I don't know if there's any quicker way to find this, but I found it on the second page of results (and I checked the others to make sure there were no other matches). Click the surname initial(s) for the full description - in this case it's IR26/932. From this description page you can order a copy, or so it says; the first step is usually to ask for a quote. On the form enter as much as you can to make it clear that you would like the full entry on fo.1879 relating to Francis Stainthorpe, from both pages of the double page spread. (IR26 documents are large books with entries written right across a double page spread, so you want to make sure you get the lot.)
OK, that's the first thing you can do. The other is to go to the British Origins website, and the National Wills Index there. This is a pay site, where you can take out subscriptions for periods from a few days to a year, though some basic searches are free.
The IR27 document indicates that there was a will proved in the Exchequer Court of York in 1822, so you should be able to find that in the index at Origins, and with these particular wills, you can order a copy online. This is provided by the Borthwick Institute in York, where the originals are held; you can also order direct from them without going via Origins, and the IR27 entry probably gives enough information for you to do this. There should be information about this on the Borthwick's own site.
Hope this helps - it's not the most straightforward kind of research!
Arthur
