Are iron injections working faster than iron tabs in replenishing the ferritin level and the general level of iron in the body?

Yes: Injections are almost always absorbed by the body more readily than oral medications. However, as long as your doctor does not believe your iron level is dangerously low, taking oral iron is adequate. It is best absorbed with vitamin C (citrus), three times per day. Be aware that it will turn the stool black and if it causes constipation, you might try a different type of iron - iron gluconate.