Die Kollegin, deren Schreibtisch neben meinem steht, sagt, ich solle den Kassenbon lieber noch eine Woche aufheben.

Deren is the relative pronoun meaning whose.

So:

Die Kollegin, deren Schreibtisch neben meinem steht, ...
= The colleague whose desk is next to mine ...

A useful point: deren refers back to die Kollegin, so it agrees with the person being referred to, not with Schreibtisch.

• antecedent: die Kollegin → feminine singular
• relative pronoun for possession: deren → whose

This is the genitive relative pronoun.

In a relative clause, German normally uses a relative pronoun, not a regular possessive like ihr.

So:

• die Kollegin, deren Schreibtisch ... = the colleague whose desk ...
• ihr Schreibtisch would mean her desk, but it would not properly introduce the relative clause here

You need deren because the clause is attached to die Kollegin and describes her.

The noun Schreibtisch is simply omitted because it is understood from context.

Full version:

deren Schreibtisch neben meinem Schreibtisch steht

But German, like English, often avoids repeating the same noun:

• neben meinem = next to mine
• understood meaning: next to my desk

So meinem stands in for meinem Schreibtisch.

Because neben takes the dative when it describes location, and here it means a fixed position: the desk is located next to another desk.

The implied noun is Schreibtisch, which is masculine:

• der Schreibtisch
• dative singular: dem Schreibtisch
• with mein: meinem Schreibtisch

So:

neben meinem
= next to mine / next to my desk

If motion were involved, neben could take the accusative instead, but not here.

German often uses position verbs where English just uses is.

For furniture and many physical objects, stehen is very common when something is standing in a place:

• Der Schreibtisch steht am Fenster.
• Die Lampe steht auf dem Tisch.

So deren Schreibtisch neben meinem steht is very natural German.

English would usually say whose desk is next to mine, but German prefers steht here.

Because that part is a relative clause, and German sets relative clauses off with commas.

Main structure:

Die Kollegin ... sagt ...

Inserted relative clause:

deren Schreibtisch neben meinem steht

So the commas mark the beginning and end of the extra descriptive clause.

Solle is Konjunktiv I, which is very commonly used for indirect speech or reported speech.

So:

Sie sagt, ich solle den Kassenbon aufheben.
means roughly: She says I should keep the receipt.

It reports her words or advice without presenting them as the speaker’s own direct statement.

Compare:

• ich soll = more direct, common in everyday speech
• ich solle = more formal, more clearly reported speech

In news, formal writing, and careful narration, Konjunktiv I is especially common.

German often omits dass when using indirect speech with Konjunktiv I.

So both of these are possible:

• Die Kollegin sagt, ich solle den Kassenbon aufheben.
• Die Kollegin sagt, dass ich den Kassenbon aufheben soll.

The first version is more compact and more clearly marked as reported speech because of solle.

The second version is also very normal, especially in everyday German.

Because aufheben is an infinitive, and in this clause it goes to the end.

The key verb here is:

• solle = finite verb
• aufheben = infinitive

German puts the infinitive at the end of the clause:

ich solle den Kassenbon ... aufheben

Also, aufheben is a separable verb in many finite forms:

• Ich hebe den Kassenbon auf.

But when it appears as an infinitive, it stays together:

• ... den Kassenbon aufheben

Here lieber means something like:

• rather
• preferably
• better
• had better

It makes the advice sound like a recommendation:

ich solle den Kassenbon lieber noch eine Woche aufheben
= I should probably keep the receipt for another week / I’d better keep it for another week

So lieber adds the sense that this is the wiser option.

Here noch eine Woche means for another week or one more week.

So the idea is not just keep the receipt, but keep it for one additional week.

Examples:

• noch einen Tag = one more day / for another day
• noch einen Monat = one more month / for another month

Because Kassenbon is masculine:

• der Kassenbon

And it is the direct object of aufheben, so it must be in the accusative:

• nominative: der Kassenbon
• accusative: den Kassenbon

So:

den Kassenbon aufheben
= keep the receipt

No. German has several common words, depending on context:

• der Kassenbon = receipt from a cash register, shop receipt
• der Bon = shorter, very common in everyday speech
• die Quittung = receipt, often more formal, sometimes specifically proof of payment
• der Beleg = receipt/document/proof, often used in business or accounting contexts

In this sentence, Kassenbon is very natural for a store receipt.

It is grammatical and natural, but it sounds a bit more careful or written because of ich solle.

A more everyday version would often be:

Die Kollegin, deren Schreibtisch neben meinem steht, sagt, ich soll den Kassenbon lieber noch eine Woche aufheben.

Or:

... sagt, dass ich den Kassenbon lieber noch eine Woche aufheben soll.

So the original sentence is not unnatural at all; it is just a little more formal in tone because of the reported-speech form solle.