אחרי ששילמנו, הוא השאיר טיפ קטן למלצר.

In Hebrew, ש־ often introduces a subordinate clause. After אחרי, the combination אחרי ש־... means after ... followed by a full clause.

So:

• אחרי ששילמנו = after we paid
• literally, something like after that we paid

This is a very common pattern:

• אחרי שאכלנו = after we ate
• אחרי שדיברתי איתו = after I spoke with him

Without ש־, you would usually need a noun instead of a full clause, for example:

• אחרי התשלום = after the payment

שילמנו is the past tense form of לשלם (to pay).

The ending ־נו is the key part here: it marks we in the past tense.

So:

• שילמתי = I paid
• שילמת / שילמתָ = you paid
• שילם = he paid
• שילמה = she paid
• שילמנו = we paid

So even without the pronoun אנחנו, the verb itself already tells you the subject is we.

Yes — Hebrew could absolutely say just השאיר טיפ קטן למלצר.

In the past tense, the verb already shows the subject:

• השאיר = he left

So הוא is not grammatically necessary here. It is often added for one of these reasons:

• for clarity
• for emphasis
• for contrast

For example, if the speaker wants to make it clear that he, not someone else, left the tip, adding הוא makes sense.

So:

• השאיר טיפ קטן למלצר = He left a small tip for the waiter
• הוא השאיר טיפ קטן למלצר = same basic meaning, but with an explicit he

השאיר is the past tense masculine singular form of להשאיר, which means to leave, to leave behind, or to leave something for someone.

In this sentence:

• הוא השאיר טיפ קטן = he left a small tip

This is the normal verb used when talking about leaving a tip, leaving money, leaving something on a table, and so on.

It is different from עזב, which usually means left in the sense of went away / departed / abandoned.

Compare:

• הוא השאיר טיפ = he left a tip
• הוא עזב את המסעדה = he left the restaurant

In Hebrew, adjectives usually come after the noun they describe.

So:

• טיפ קטן = a small tip
• בית גדול = a big house
• ילדה חכמה = a smart girl

Also, the adjective has to agree with the noun in:

• gender
• number
• definiteness

Here, טיפ is:

• masculine
• singular
• indefinite

So the adjective must also be masculine singular indefinite:

• קטן

If the noun were feminine, it would change:

• מתנה קטנה = a small gift

Because את is only used before a definite direct object.

Here, טיפ קטן is a direct object, but it is indefinite:

• a small tip, not the small tip

So no את is used.

Compare:

• הוא השאיר טיפ קטן = he left a small tip
• הוא השאיר את הטיפ הקטן = he left the small tip

That second sentence has את because הטיפ הקטן is definite.

ל־ means to or for.

So למלצר means to/for a waiter or to/for the waiter, depending on context.

This is one of those places where unpointed Hebrew spelling can be ambiguous:

• למלצר can represent לְמַלְצָר = to a waiter
• or לַמַּלְצָר = to the waiter

In normal modern Hebrew writing, both are written the same way: למלצר.

So you usually figure it out from context.

Also, notice that למלצר is not the direct object. The tip is the thing being left, and the waiter is the person it is left for.

Because the waiter is the recipient, not the thing being left.

In the sentence:

• טיפ קטן = the thing left
• למלצר = the person receiving it

Hebrew often uses ל־ for this idea of to/for someone.

This is very similar to English:

• He left a tip for the waiter
• He gave money to the waiter

So למלצר functions like for the waiter or to the waiter, not like a direct object.

It is normal and natural, because the sentence begins with a subordinate clause:

• אחרי ששילמנו, ... = After we paid, ...

This works much like English, where a comma is commonly used after an opening clause.

In informal writing, some people may leave it out, but the comma is standard and helpful.

Yes. Hebrew word order is somewhat flexible, and that version is also possible:

• הוא השאיר טיפ קטן למלצר
• הוא השאיר למלצר טיפ קטן

Both are grammatical.

The version in your sentence is a very natural default order:

1. verb
2. direct object
3. recipient / prepositional phrase

Changing the order can slightly shift the emphasis, but the basic meaning stays the same.