mousikomisyo no hikae wo nakusanai you ni, uketotta ato sugu kaban ni iremasita.

Here 控え（ひかえ） means a copy kept for reference. In forms and paperwork, it often refers to your copy of a document after submission.

So:

• 申込書 = application form
• 申込書の控え = a copy of the application form / the applicant’s copy of the form

Depending on context, English might translate it as copy, receipt copy, or duplicate.

The particle の links two nouns, and here it works a bit like of in English.

• 申込書 = application form
• 控え = copy
• 申込書の控え = the copy of the application form

This is a very common noun-modifying pattern in Japanese:

• 学生の名前 = the student’s name / the name of the student
• 会社の電話番号 = the company’s phone number

So 申込書の控え is simply a noun phrase.

Because 控え is the direct object of the verb 入れました.

The speaker put something into their bag, and that something is:

• 申込書の控えを = the copy of the application form

So the sentence is saying they put the copy into the bag.

Even though なくさないように also relates to the copy, the main action of the sentence is still かばんに入れました (put it in the bag), so を marks the thing being put in.

ように here expresses purpose or so that.

• なくす = to lose something
• なくさない = not lose it
• なくさないように = so as not to lose it / so that I wouldn’t lose it

So this part gives the reason or purpose for the action that follows:

• 申込書の控えをなくさないように、かばんに入れました。
• I put the copy in my bag so that I wouldn’t lose it.

This pattern is very common:

• 忘れないようにメモします。 = I make a note so that I won’t forget.
• 遅れないように早く出ました。 = I left early so that I wouldn’t be late.

Because なくす and なくなる are different verbs.

• なくす = to lose something
• なくなる = to disappear / be lost / be gone

In this sentence, the speaker is talking about their own action: they do not want to lose the copy. So なくす is the correct verb.

• 控えをなくさないように = so that I won’t lose the copy

If you used なくならない, it would mean something more like so that it won’t disappear / be gone, which is not the normal way to express this idea here.

Yes. The pattern is:

• Verb (negative or potential/etc.) + ように、...
• meaning so that... / in order to...

Then the second part gives the action taken for that purpose.

So:

• なくさないように、かばんに入れました。
• I put it in my bag so that I wouldn’t lose it.

This is extremely common in Japanese. A few examples:

• 風邪をひかないように、暖かくしてください。
  Please keep warm so that you don’t catch a cold.

• 見えるように、大きく書きました。
  I wrote it big so that it can be seen.

Because when a verb comes before あと, it usually appears in the plain past form to mean after doing something.

• 受け取る = to receive
• 受け取ったあと = after receiving

This is a standard pattern:

• 食べたあと = after eating
• 帰ったあと = after going home
• 見たあと = after seeing

So 受け取ったあとすぐ means:

• right after receiving it

Even though it feels like past tense in form, here it is functioning inside a time expression.

すぐ means immediately, right away, or soon.

In this sentence:

• 受け取ったあとすぐ = immediately after receiving it

It tells you the speaker did not wait. They put the copy into the bag right after getting it.

So the timeline is:

1. receive the copy
2. immediately put it into the bag

Because 入れる means to put something into a place.

With this verb:

• the thing being put in takes を
• the destination/place takes に

So:

• 申込書の控えを = the thing put in
• かばんに = into the bag

This pattern is very common:

• 本をかばんに入れる = put a book in a bag
• お金を財布に入れる = put money in a wallet

If you said かばんを入れました, that would mean I put in the bag itself, which is a completely different meaning.

Japanese often leaves out the subject when it is clear from context.

In this sentence, the natural assumption is that the speaker is talking about their own action, so the unstated subject is something like:

• 私は or 自分は

So the full meaning is basically:

• (I) put the copy of the application form into my bag right after receiving it so that I wouldn’t lose it.

Omitting the subject is extremely normal in Japanese and does not make the sentence incomplete.

A helpful breakdown is:

• 申込書の控えを
  the copy of the application form

• なくさないように、
  so that I wouldn’t lose it

• 受け取ったあとすぐ
  immediately after receiving it

• かばんに入れました。
  I put it in my bag

So the overall structure is:

[object] + [purpose] + [time] + [main action]

Japanese often places background information such as purpose, reason, and time before the main verb at the end.

Yes, in many cases Japanese word order is flexible as long as the particles make the relationships clear.

For example, these are all quite understandable:

• 受け取ったあとすぐ、申込書の控えをなくさないように、かばんに入れました。
• 申込書の控えを、受け取ったあとすぐ、なくさないようにかばんに入れました。

But the original order is very natural and easy to follow.

In general, Japanese tends to put the main verb at the end, while the earlier parts can move around for emphasis or flow.

They are similar, but not always interchangeable.

Here なくさないように is the natural choice because it expresses taking care so that something undesirable does not happen.

• 忘れないように
• 遅れないように
• なくさないように

This kind of negative precaution often sounds especially natural with ように.

You may learn that ために also means for or in order to, but it is not used in exactly the same way in every sentence. In this sentence, なくさないために is possible in some contexts, but なくさないように sounds more like so that I wouldn’t lose it / to make sure not to lose it, which fits very well.

It is polite but plain in content.

The main verb is:

• 入れました = polite past

So yes, the sentence is in a polite style overall.

The parts before it use plain forms because that is normal inside modifiers and grammar patterns:

• なくさないように
• 受け取ったあと

This mixture is completely standard in Japanese. The final verb usually determines the sentence’s politeness level.