הספרים שלהם על השולחן.

Because Hebrew usually does not use a present-tense form of to be in simple sentences like this.

So:

הספרים שלהם על השולחן
literally looks like: their books on the table

but it naturally means: Their books are on the table.

In the past or future, Hebrew does use forms of to be, for example:

הספרים שלהם היו על השולחן = Their books were on the table

Word by word:

• הספרים = the books
• שלהם = their / of them
• על = on
• השולחן = the table

So the structure is basically:

the books of them on the table

which is the normal Hebrew way to express Their books are on the table.

This is a very common question.

In Hebrew, with the של possession pattern, the possessed noun often still takes the definite article:

• הספרים שלהם = their books
• literally: the books of them

So even though English does not say the their books, Hebrew does say the books of them.

If you remove ה־ and say ספרים שלהם, it often sounds more like some books of theirs or a less clearly definite phrase.

Because Hebrew possession is often built as:

noun + של/possessive form

So instead of English their books, Hebrew commonly says something closer to:

the books of them

That is why:

• English: their books
• Hebrew: הספרים שלהם

This word order is completely normal.

שלהם means their or theirs, and it agrees with the owners, not with the thing being owned.

Here, שלהם refers to plural masculine or mixed-gender owners.

That means:

• שלהם = their for they (masculine/mixed)
• שלהן = their for they (feminine)

So the form depends on who owns the books, not on the fact that books is masculine plural.

Because שלהם is used for:

• masculine plural
• or mixed-gender plural

If the owners were an all-female group, you would use:

• שלהן

So:

• הספרים שלהם = their books (for masculine/mixed owners)
• הספרים שלהן = their books (for feminine owners)

על השולחן means on the table.

It is the location phrase in the sentence.

So the sentence has two main parts:

• הספרים שלהם = the subject idea, their books
• על השולחן = where they are, on the table

This is a very common Hebrew sentence pattern:
[noun phrase] + [place/state]

Because על means on, while ב־ usually means in / at.

So:

• על השולחן = on the table
• בשולחן would not mean the same thing and is generally not what you want here

If something is resting on the surface of a table, על is the natural preposition.

Because השולחן means the table, a specific table.

So:

• השולחן = the table
• שולחן = a table / table

Since the meaning is on the table, Hebrew marks that with ה־.

Also notice that על is a separate word, so the ה־ stays on the noun:

• על השולחן

Yes. It is a completely normal, complete Hebrew sentence.

In present-tense Hebrew, sentences like this are called nominal sentences: they can have a subject and a predicate without an expressed is/are.

So הספרים שלהם על השולחן is just as complete and natural in Hebrew as Their books are on the table is in English.

Yes.

Two common alternatives are:

הספרים שלהם נמצאים על השולחן
This explicitly includes נמצאים = are located / are found.
It is grammatical, but often less natural than the shorter version in everyday speech.

ספריהם על השולחן
This uses a more formal/literary possessive form meaning their books.
It is correct, but it sounds more formal than הספרים שלהם.

For ordinary modern spoken Hebrew, הספרים שלהם על השולחן is very natural.

A simple transliteration is:

ha-sfarim shelahem al ha-shulchan

A few pronunciation notes:

• הספרים = ha-sfa-RIM
• שלהם = shela-HEM
• השולחן = ha-shul-CHAN

The ch in shulchan is the throaty sound heard in words like German Bach or Hebrew ח.