Hello, Ammar!
. . .
No, their truth-table values are not identical.
Do you understand the difference between "A is equivalent to B" and "A implies B"?
"A implies B" says that if A is true then B must be true but says nothing about what happens if A if false.
"A is equivalent to B" says that if A is true then B must be true and if A is false then B is false".
In order that (p->r)^(r->q) be true both p->r and r->q must be true. In that case, if p is true, r is true and then q is true. In other word, if p is true so is q: p->q.
But (p->r)^(r->q) is false one of p->r or r->q must be false. It might be the case, for example that p is true and r is false, so that p->r is false. That tells us nothing about whether or not q is true or false.