Done. Let's check, if it was done right:
Original sponge, half of year ago, note the dieing ends:

Before blending it was 3"x2", trunk and the base of branches.
Procedure:
1. Peroxidized blender.
2. Prepared the 1.025 SG saltwater in 1% solution of peroxide.
3. Filled to the 2/3 the blender cup by this solution.
4. Wrapped the sponge in the double big coffee filters, while in the tank. No contact with air.
5. Removed, moved into the blender cup, removed the wet paper underwater.
6. Blended at low speed several times, in short duration each. The pulse didn't chop, then used chop mode.
7. Filtered through new 250 micron filter bag (it's finer, than brine shrimp net, but has larger mesh, than polyester fabric. Wal-Mart had only dyed kinds), in another acrylic glass.
8. Filtered this liquid through the piece of the BA filter floss roll, underlined by 50 micron filter pad, just in case if the floss is too loose, more particles will be caught by the fine polyester pad.
9. Placed to the critters box, filled by tank water.
10. Remaining liquid seemed to still be cloudy, used another 50 mk pad for one more filtering. This pad was placed onto the previous pads in the critters box.
All time of a keeping sponge in the peroxide was within 2 min.
11. The critters box was placed in the 20g established skimmed tank, fishless, but with hermits, corals and macroalgae. 4 hrs in the box to guarantee the low flow.
The only problem: box tried to flow, had to weight it down by stone.
12. Skimmer started to overflow and collect the orange-red skimmate.
13. After 4 hrs, the pads were removed from the box, placed beside the 150 gph Mini-Jet 606 (high flow, but not in direct blast), weighed down by the same Fiji LR branch.
The filtered cells looks on the pad as a slight hint of yellow-orange.
As an afterthought, the big pads are quite unsightly in the tank, may be I should use the smaller pieces, like 1"x1", only have no small funnels to hold such a small pieces.
Correct, please, if anything was done improperly.
Anyway, only piece of sponge 1"x0.5" is left now, too little for a new experiment.