It says in SA OC Siman 539 Sif 11 (in the Rema) that one may buy things on Chol HaMoed that are needed for the Yom Tov Sheini (of the last days of Yom Tov), which is rabbinic in nature for those living outside of Israel, and is not Yom Tov at all for those living in Israel. Rebbe Akiva Eager there writes that the Tur says one is permitted to "prepare". Rebbe Akiva Eager then says that the Tur is implies that even something that is a malacha, like cooking, may be done on Chol HaMoed for Yom Tov Sheini.
In M"B Sif-Katan 38, the author writes that we don't say "yom tov sheini might really be a weekday and therefore it is ossur to do something chol hamoed for its needs". Rather, it is muter to do something on Chol HaMoed for the purpose of Yom Tov Sheini.
My question is: Is an Israeli keeping only 7 days of the Chag allowed to cook on Chol HaMoed for someone else's Yom Tov Sheini (which is Isru Chag for the one cooking)? Even though the Yom Tov Sheini will be a weekday for the one cooking, for the other person it's Yom Tov and would have the heter of the Rema and Rebbe Akiva Eager (with the explanation of the M"B). What sources are there on this? What savarah (logic) could be said (in favor of one way or the other)?