Spin Off from Bucko

So how would this work.

すぐ里絵子はどうのか説明する国管理局の手紙を貰ってきます。
You should soon come to recieve a letter from immigration that will explain what to do.



What would be a better to way to say that? I know I could remove てくる I know there is another verb which means 貰う.

Or how about

手紙来ませんか？そう、今日全ての書類は日本に送ってきますっていったEメールを貰いました。
You didn't get a letter? Really? I got an email stating all documents would be sent to Japan.

I really wanted to say I got an email saying the petition was completed and will be filed with the US Embassy in Japan.

You should soon come to receive a letter from immigration that will explain what to do.

This is how I would translate it (loosely)
恵理子は（ＩＭＭＩＧＲＡＴＩＯＮ）から手続きを説明する手紙をそのうち受け取るはずでしょう。

手紙来ませんか？そう、今日全ての書類は日本に送ってきますっていったEメールを貰いました。
You didn't get a letter? Really? I got an email stating all documents would be sent to Japan.

手紙はまだ届いてないんですか？ ありえないんでしょう。全部の書類が日本に届けられるだろうというＥメールを貰いましたから。。。

Note that you can't really say 手紙来ませんか？in this situation. This would mean something like "Won't the letter come"? instead.