She was first female president to be elected in 1919.
Does the meaning of this sentence same as
She was first female president who was elected in 1919.
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They do mean the same thing, however, the first is much more idiomatic.
What they mean is that, of all of the female presidents elected in 2019, she was the first.
One other thing I'll mention is that these have a completely different meaning to something like:
She was the first female president [of some country], and was elected in 2019.
Elected in 2019, she was the first female president [of some country].
Both of these tell us that she was the first female president of all time, and also specify the year in which she was elected.