Is it valid for I'tikaf if the intention is made after entering the mosque?

For the validity of I'tikaf, a prior intention before entering the mosque is not a condition. Rather, I'tikaf is valid whenever a Muslim intends to stay in the mosque seeking closeness to Allah Almighty, even if the intention is made after entering it, because "actions are but by intentions." I'tikaf is defined as staying in the mosque with the intention of drawing closer to Allah Almighty. So, whenever the intention and the stay in the mosque are present, the I'tikaf is valid.