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The "best time" is based on personal views, especially when you are talking about wanting to hit reward goals on multile cards. The PRG would be a good card, but would need to apply when it makes sence to you.
Oh and her FICO scores are in the 700s. I was wondering whether her closed account with AmEx, or the 2 recent credit cards, 1 car loan and 1 mortgage would have an affect...
They were all acquired between May and November 2014.
No late or derogs on her reports and based off the info your provided I would say she would be highly approved...
Did she ever have any lates with Amex ever? They do have a very long memory...
Also check Amex pre-qual site, I bet she is good to be for any charge; green, gold or platinum!
Keep us posted...