Moves 12 to 24 in demo https://online-go.com/demo/view/564614 show the tactic of “creeping along the edge”, which as shown in moves 15-20 is difficult to block.
Do we have to avoid the hole at J4 at all costs, or is there a good way for black to block move 12?
Have you tried h6 instead of h5?
If you have not already blocked at j4, then you are accepting giving up a bit of the edge. I think something like h6 gives away the minimum.
I was about to say H6 too.
I see this, thanks, but what are the best followup moves for black H6? I can’t see where it can lead.
W J6
B J7 atari
W J5 connects
B H7 connects
W H5 pushes
B G5 blocks
I’m on smartphone and I have trouble moving back and forth from forum to demo
Lys, I’ve shared this variation. It looks to me like a big failure for black. Did I misunderstand your moves?
First picture by @teapoweredrobot
teapoweredrobot, Thanks for the pictures. It is all clear to me now. I wish I knew how to make images of Go boards.
Having a demo board, it’s just a screenshot.
Actually I could have done it myself on your demo board, even using a smartphone.
I didn’t think about it, sorry. 
Also pasting in the forum is easy as CTRL+C (on PC… with a smartphone you have to use “upload”)
Test. Hmmm, Ctrl+C does nothing. I suppose I could take a screenshot then upload it as an image.
And then CTRL+V
but yes, I’m on my phone so just screenshot, crop, upload.
You’re welcome!
Sorry, my mistake: Ctrl+C copies, Ctrl+V pastes.
They are generic shortcuts for copy and paste.
On Discourse (this forum) works fine.
Same for right-click copy and paste.
Easier than save file + upload.
To answer the actual question here though:
Black playing at j4 is a big endgame move so typically important to play. But “at all costs”? Never! If black has something that will gain more than the ~7 points letting white play j4 will cost then do that.
It’s just that in many endgame scenarios nothing else will be worth losing 7 points in gote.
