Hello @JusGellin
NO. Not at this time. It 'may' show up with support in the future if its developers deem appropriate. So, currently, it is a WoofCE Puppy exclusive.
Hark! Look at what the KL developers have done for you.
The KL's developers have done, for you and members, a VERY GOOD solution. AS such, their solution, like SAVESPEC, works like a charm, as well. OOTB, the KLs boot menu is pre-designed for your use and is, IMHO, a solution that does EXACTLY what you are doing. They have pre-structured to make booting, with session management, simple for ALL of the KLs. And its the same for each of the KLs.
If you follow their OOTB model, it can be used for EVERY forum distro, like WoofCE, that offers session-management which is what it appears you desire. Thus a single, one-time, solution where its obvious.
Do this and you will understand session-management for all forum distros. They made this so simple and its built-in to their boot strategy for simple operation with little need for user involvement when booting.
I repeat: If you are willing to follow their model, pre-designed, it can be used for ALL forum distros.There is no magic, no necessity for ever changing, no need to change anything as it is so OBVIOUS (like SAVESPEC does).
Done once for the lifetime of your PC(s) for ALL future distros use. (To be clear, you ONLY do this once!!!) You must;
Create a partition labeled Persistence (not 'SAV' as you show. In fact, a single command can be used to change the label you have to 'Persistence')
On the Persistence partition, create a folder named Sessions
As you can see, this naming "Sessions folder on the Persistence partition" make a very obvious understanding of what you use that for.
That's it! That will cover all future use for any forum distro you ever boot from the forum. All of this make booting simple for use in booting KLs and WoofCE Pups.
Beside all the words, I have explained this several time to the forum for about 5 years now.
Repeating, this is what I do for every PC I ever get ... Again this is only done ONCE for any given PC as this is a permanent area for ALL sessions to be kept.
Make a Persistence partition on its system drive
Create a Sessions folder on the partition
And all of my KLs and PUPs use this, OOTB, forevermore. This is so obviously simple and so obviously foolproof. Its brilliant! Credit goes to the KL people (@wiak, @rockedge, @fredx181, @Sofiya) and to @gyrog with the WoofCE team.
Boot WoofCEs as their SAVESPEC points there. Boot KLs as their boot menus point there. Simple and solved ... Once!
Lastly, no boot menu changes are necessary for the booting distro to find its session during boot.
Enjoy