Can't brew today with starter made

Hey everyone, something came up today and I'm not able to actually brew. The starter is in a flask with a foam stopper. Am I OK to just throw this in the refrigerator for a week? Should I change out the foam stopper for something else?

Id swap the foam stopper for a closed rubber one or at least an airlock. The yeast will be fine but you may have some lag time due to inactivity. If I were you Id stick it in the fridge and take it out to decant 2-3 days before brew day. Id then add back some new starter wort to get them going again and get you more yeast cells. But even if you just pitched it from the fridge, it would probably still be ok

Well, yeah, that's cold crashing. That's what you wanna do so the yeast can fall/separate from the wert.
Leave the foam stopper in, spray on some Starsan and cover with some tin-foil.
You'll be good to go in a week. On brew day, decant, let it come close to room temp. then pitch.

I've been in this situation many times and usually I take a litre or so of wort about halfway into the mash (easy since I have a recirculating system). I boil it for about 10 minutes, cool it and pitch into the decanted starter. Usually I have a small krausen by the time I'm ready to pitch.

I'm sure it's not necessary, but I like to play it safe.

If you have as much starter as you want, then the fridge is the best place to separate the yeast from the wort anyway. If you might want more, then you have time to build the starter up a bit before crash cooling.

I routinely just stick my foil-covered beaker in the fridge for 1-7 days after the starter is finished