"So, if I understand well, if I would transfer everything to the fermentor, I would have a total volume of 6 gallons (liquid+trub) of 1.089. Does the yeast "eat" sugars "hidden" into the solids? Then, any solid would be a part of the yeast cake to finally ends with my 4.9 gallons of solid."
No. You won't get 6 gallons of 1.089. The gravity isn't going to increase just from dumping it from 1 container to another.
The gravity is only going to go up if you concentrate the sugar by boiling off more water. If you lose some wort to trub, hops etc you are losing both water and sugars.