atena wo kakanai mama denpyou wo dasite simatte, kakinaosimasita.

Sure:

• 宛名 = the addressee / recipient name (sometimes loosely address label depending on context)
• を = marks the direct object
• 書かない = do not write
• まま = while still in that state / without changing that state
• 伝票 = a slip, form, invoice, shipping label, waybill, etc. depending on context
• を = marks the direct object again
• 出して = submit / hand in / send out
• しまって = adds the nuance of ending up doing it, often with regret or as a mistake
• 書き直しました = rewrote it / wrote it over again

So the structure is basically:

• Leaving the addressee unwritten
• I went ahead and submitted the slip
• and then rewrote it

Vない + まま means without doing V, and remaining in that state.

So:

• 書かない = not write
• 書かないまま = without writing it, or more literally, leaving it unwritten

The nuance is important. It is not just that the writing did not happen; it emphasizes that the next action happened while that blank state continued.

So 宛名を書かないまま means:

• without writing the addressee
• with the addressee still left blank

That is why it fits well in a sentence about making a mistake on a form.

They are similar, and both can often be translated as without writing.

But there is a nuance difference:

• 書かずに focuses on not doing the action
• 書かないまま focuses on the unchanged state that remains

So:

• 宛名を書かずに伝票を出した
  = I submitted the slip without writing the addressee.

• 宛名を書かないまま伝票を出した
  = I submitted the slip with the addressee still left blank.

In this sentence, まま feels very natural because the problem is exactly that the form remained incomplete.

Because there are two different verbs, and each one has its own direct object.

1. 宛名を 書かない

   • 宛名 is the thing being written

2. 伝票を 出してしまって

   • 伝票 is the thing being submitted/handed in

So the sentence contains two small verb phrases:

• 宛名を書く
• 伝票を出す

Each verb can take its own object, so using を twice is completely normal.

出す has many meanings in Japanese, and one very common one is to submit / hand in / send out / issue depending on context.

So 伝票を出す does not usually mean literally take a slip out here. It more likely means something like:

• submit the form
• hand in the slip
• send off the shipping label
• file/process the invoice

The exact English depends on what kind of 伝票 it is:

• shipping slip
• invoice
• receipt/form
• order slip

So this is a good example of how 出す often has a more abstract meaning than just physical movement.

〜てしまう often adds one of these nuances:

1. completion — doing something completely
2. regret / mistake / unintended result — ended up doing
3. sometimes both at once

Here, the second nuance is the important one.

• 伝票を出して = submitted the slip
• 伝票を出してしまって = ended up submitting the slip / went and submitted the slip

It suggests that this was a mistake or something the speaker wishes had not happened.

That fits the next part:

• 書き直しました = rewrote it

So the sentence has the feeling of:

• I accidentally/incorrectly submitted the slip without writing the addressee, so I had to rewrite it.

Also, the て in しまって connects this clause to the next one.

The order is:

1. The addressee was not written.
2. In that incomplete state, the slip was submitted.
3. After that, it was rewritten.

So the timeline is:

• 宛名を書かないまま
  = with the addressee still not written

• 伝票を出してしまって
  = I ended up submitting the slip

• 書き直しました
  = then I rewrote it

A natural way to understand it is:

• I submitted the slip without writing the addressee, and then rewrote it.

Because of しまって, it can also sound like:

• I mistakenly submitted the slip without writing the addressee, so I rewrote it.

Japanese often omits things that are clear from context.

In 書き直しました, the sentence does not explicitly say:

• who rewrote it
• what was rewritten

But from context, we naturally understand:

• the subject is probably I
• the thing rewritten is probably the slip/form, or at least the part that had to be written again

So English often has to add something:

• I rewrote it
• I filled it out again
• I rewrote the form

Japanese leaves that unsaid because it is already obvious from the previous clause.

書き直す means to rewrite or to write again correctly.

It is made from:

• 書く = write
• 直す = fix, correct, do again

So 書き直す is more specific than 直す.

Compare:

• 直しました = corrected it / fixed it
• 書き直しました = rewrote it

In this sentence, the problem was related to writing on a form, so 書き直しました makes it clear that the correction involved writing it over again, not just fixing something in a general way.

So it is a very natural choice here.