Hi Janulka. I personally don't think there will be enough blackberry juice left in the pulp once it has been strained, to use in a TC. I have just made a country wine recipe using fresh peaches and I mashed them down to a pulp before straining through a muslin cloth into a DJ and placed an airlock in the top. The peach pulp left didn't look like it could be used so I put it on my compost heap to break down.
There may well be someone along here shortly, with more knowledge than me and tell you something different.
I am looking to make a dark fruits TC using blackcurrants and blackberries, but am having trouble finding a 100% blackcurrant juice. In Tesco and Sainsburys you can buy Copella blackberry and apple which is 100% juice. Might have to use Ribena which is 35% juice, or resort to using real fruit.