1) The cost is from China to France's post office. Peter need to pick up the goods from post office by himself.
2) The cost is only to France post office. Peter needs to pick up the goods from post office himself.
Well, it's not exactly clear what you mean by 'second sentence'. If you mean the second sentence on the page, there are three mistakes: Peter need to pick up the goods from post office by himself.
If you mean the two sentences of example #2, then there are two mistakes.
The cost is only to France post office. Peter needs to pick up the goods from post office himself.
Context is always important; labelling is rarely important.
I meant sentence No. 2. And I agree with you on the second mistake (the is missing). But, regarding the first mistake you underlined, is it possible to justify it this way and say "France post office" is the name (a proper name)? If we take it this way, can't we say it's correct?
No
Context is always important; labelling is rarely important.