How does しまう function here and/or what does it mean?


I've frequently encountered problems with しまう. Usually it appears alongside て
form, like 遅れてしまいました, "Unfortunately I came too late". In this case, it
signals regret on the speakers behalf.

I'm having far more issues with this verb when its like here:
母からの手紙は箱の中に大切にしまってあります。

I can't even translate this sentence. I think the speaker says that his mom's
letter is precious to him out of all the things in the box. But really, I
don't know how to incorporate a meaningful interpretation of しまう here. Maybe
like "ultimately is precious"? The て-form with ある also kind of gives me a
headache. Maybe it means that the letter has reached the status "precious" and
stays in that status now? It's one of the functions I learned for て form + いる.
Like 窓が困っている (or ある, because its an object? I once learned that いる is for
living beings and ある for objects. But I feel like いる might have been combined
with non-living objects too already. My memory might deceive me on this
though...^^).




> 母からの手紙は箱の中に大切にしまってあります。

The verb しまう（仕舞う） here is used in the sense of "put away, keep, store
(something somewhere)". It's explained in definition #3 in
[デジタル大辞泉](http://dictionary.goo.ne.jp/jn/100617/meaning/m0u/%E4%BB%95%E8%88%9E%E3%81%86/):

> しまう【仕舞う】  
>  ３ 使用したもの、大切なものなどを元の場所や入れ物などの中に納める。かたづける。「夏物を **しまう** 」「雛人形を **しまう** 」「胸のうちに
> **しまっ** ておく」

～てある indicates a resultant state. しまってある here, which consists of the te-form
of しまう + subsidiary verb ある (or, verb しまう + conjunctive particle て +
subsidiary verb ある), means that 母の手紙 has been put away in 箱 some time ago and
is still in the 箱.

* * *

As to the difference of "intransitive verb + ている" and "transitive verb + てある":

Intransitive + ている -- _current state_ (NOTE)

  * 「窓が閉まっている」 The window is closed. 
  * 「窓が開いている」 The window is open. 

Transitive + てある -- _resultant state_

  * 「窓が/を閉めてある」 The window has been closed some time ago and is still closed. → The window has been / is kept closed. / We keep the window closed. 
  * 「窓が/を開けてある」 The window has been opened some time ago and is still open. → The window has been / is kept open. / We keep the window open. 
  * 「手紙が/をしまってある」 The letter has been put away somewhere some time ago and is still stored there. → The letter is stored / I keep the letter somewhere.

For more, see [this thread](https://japanese.stackexchange.com/q/5505/9831).

NOTE: As you may already know, ～ている can also indicate "continuous/ongoing
action", eg 走っている (is running). And of course we also have "transitive + ている",
eg 本を読んでいる, 店を閉めている.

