translation - Confused about って in this sentence

A man and a woman who had undergone hardship together as children before being forced to part meet again and remember their last words to each other.

The woman says:

生きてて良かったって、心の底から思える瞬間って、どんな感じかしら？

I think the first part of the sentence

生きてて良かったって

means

“It’s good to keep on living”

the って here being a quotative particle since 生きてて良かった was the last thing the man said to the woman. (Please correct me if I’m mistaken).

The second part

心の底から思える瞬間って

confuses me. What is the function of the って here? It doesn’t seem like a quotative particle. I guess it translates to something like:

a moment that seemed to come from the bottom of your heart.

And I think the last part

どんな感じかしら？

translates as:

Was that your feeling, I wonder?

So, I think the meaning of the sentence (idiomatically) is something like:

You said, “It’s good to keep on living”, like you really believed it. Was that what you were feeling, I wonder?

Is this correct and what is the function of って in the second part of the sentence?

Answer

生きてて良かったって、心の底から思える瞬間って、どんな感じかしら？

These two って's are not the same.

The first って is a quotative particle. From デジタル大辞泉:

って 1⃣［格助］
１ 引用する語、または文の下に付いて、次に来る動作・作用の内容を表す。…と。「金を貸してくれって頼まれた」「読書しろって言われた」

The って is a quotative particle and means と. The two example sentences given in the dictionary can be rephrased as 「金を貸してくれと頼まれた」「読書しろと言われた」. って is more colloquial than と.

And the second is a binding particle (係助詞). From the same dictionary:

って 2⃣［係助］
１ ある事柄を話題として取り上げて示す意を表す。…は。…というのは。「あなたって親切な人ね」「彼ってだれのこと」

The って is used to introduce something as a topic. Means ～は or ～というのは. The examples can be rephrased 「あなたは親切な人ね」「彼というのはだれのこと」. って is more colloquial than は or というのは.

So your sentence can be rewritten as:

『生きてて良かった*』と、心の底から思える瞬間というのは、どんな感じかしら？

lit. Speaking of the moment when you can feel "I'm lucky to be alive" from the bottom of your heart, how would it feel? / what would it be like?
⇒ I wonder what the moment would be like when you can feel from the bottom of your heart "I feel lucky to be alive. / Thank God I'm alive."

*The た in ～～よかった here is the modal た, explained here: Usage of plain i-adjectives or た form (悪かったｖ悪い、良かったｖいい etc）

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Breakdown:

生きてて -- lit. I'm alive (and) → to be alive
良かった -- (I find it) good.
って、-- quotative
心の底から -- from the bottom of your heart
思える瞬間 -- the moment you can feel
って、-- topical

どんな感じかしら？ -- What would it be like?