Die Fernleihe kommt in meiner Wunschbibliothek an.

The verb is ankommen, which means to arrive.

In a normal main clause, German separable verbs split:

• kommt = the conjugated part
• an = the separable prefix

So Die Fernleihe kommt ... an is the present-tense form of ankommen.

Because ankommen is a separable verb.

In German main clauses, the main verb goes in second position, and the separable prefix moves to the end:

• Die Fernleihe kommt in meiner Wunschbibliothek an.

If you used the infinitive or a subordinate clause, the verb would stay together:

• ... weil die Fernleihe in meiner Wunschbibliothek ankommt
• ... um in meiner Wunschbibliothek anzukommen

No. An belongs to the verb ankommen, not to the noun phrase.

So the sentence breaks down like this:

• Die Fernleihe = subject
• kommt ... an = verb
• in meiner Wunschbibliothek = location

A learner might accidentally read Bibliothek an as a unit, but that is not what is happening here.

Because after ankommen, the place of arrival is normally expressed as a location, so in takes the dative here.

That is why you get:

• in meiner Wunschbibliothek

Compare:

• Ich gehe in meine Wunschbibliothek. = motion into the library
• Ich komme in meiner Wunschbibliothek an. = arrival at that location

So even though arrival involves movement in real life, German treats the destination here as the place where the person or thing ends up.

Because Wunschbibliothek is feminine, singular, and here it is in the dative case.

So:

• nominative: meine Wunschbibliothek
• dative: meiner Wunschbibliothek

The form meiner is the correct dative feminine form of mein.

German and English do not match prepositions word for word.

In English, at is very common for places like libraries, stations, schools, and so on. In German, in is often natural with buildings or institutions when you mean arrival there or presence there:

• in der Bibliothek
• in der Schule
• im Büro

So in meiner Wunschbibliothek is normal German, even if English would often prefer at my preferred library.

It is a compound noun:

• Wunsch = wish, preference, desired choice
• Bibliothek = library

So Wunschbibliothek means something like:

• preferred library
• library of choice
• chosen library

German often builds nouns this way by combining words into one longer noun.

Because German compound nouns are normally written as a single word.

So:

• Wunschbibliothek is correct
• not Wunsch Bibliothek

Also, the last part of a German compound determines the grammatical gender. Since Bibliothek is feminine, Wunschbibliothek is feminine too.

Because Fernleihe is a feminine noun.

So in the nominative singular, you say:

• die Fernleihe

In library context, Fernleihe usually means interlibrary loan. Depending on context, it can refer to the service/process or to the requested loan item itself. In this sentence, it is being treated as the thing that arrives.

Yes. German main clauses are flexible, as long as the finite verb stays in second position.

For example, you could also say:

• In meiner Wunschbibliothek kommt die Fernleihe an.

That puts more emphasis on the location. But kommt still stays in second position, and an still stays at the end.

Grammatically, it is present tense, but German often uses the present tense for future events when the context is clear.

So Die Fernleihe kommt in meiner Wunschbibliothek an can mean:

• The interlibrary loan arrives at my preferred library
• The interlibrary loan will arrive at my preferred library

If you want to emphasize that it has already arrived, you would use:

• Die Fernleihe ist in meiner Wunschbibliothek angekommen.