Hi Philip
If you have paid your £5 donation to yffor.com it is going to be easier to take you further back in your family tree. Don't worry I made some big mistakes when I started and there are some real howlers on Ancestry.com.
Click on "Cemeteries" at the top of the page. Go down to the line starting "Bryncroes (1886)" move across to "1813-1884" and left click on it. The searchable database will open. If you want to find Henry's burial record I suggest pressing on "Name" at the top which will rearrange the christian names alphabetically. Go to the bottom of the table where the arrows are and keep pressing the right one until you reach the Henrys and you should find yours under ID85.
You can do the same by pressing on all the table headings, try "Abode" and look for "Bodgua" and its variations. You should find Anne Hughes ID545.
Next try finding Henry II's parents. We know he was 38 when he died in 1819 which would indicate he was born around 1782.
Press "Church/Chapel" at the top of the page, go down to "BRYNCROES REGISTER OF BAPTISM" and across to "1732-1799" left click on it. Again click on the heading "NAME" and search for the Henrys look for a father whose christian name is "Griffith" and you have the baptism record ID 354. You now have his parents, abode and father's occupation.
Let me know how you get on
All the best
Glyn