Он способный инспектор.

In Russian, the verb to be is usually omitted in the present tense.

So:

• Он способный инспектор literally looks like He capable inspector
• but it means He is a capable inspector

This is completely normal in Russian. Compare:

• Он студент = He is a student
• Она врач = She is a doctor

If you talk about the past or future, a form of быть appears:

• Он был способным инспектором = He was a capable inspector
• Он будет способным инспектором = He will be a capable inspector

Here способный means something like:

• capable
• able
• talented
• competent

With a profession noun like инспектор, the most natural English idea is usually capable or competent.

So Он способный инспектор means that he is good at his job as an inspector.

It is not exactly the same as умный (smart/intelligent). Someone can be intelligent, but способный emphasizes ability or talent.

Because it is a full adjective agreeing with инспектор.

In this sentence:

• инспектор is masculine
• singular
• nominative

So the adjective also has to be:

• masculine
• singular
• nominative

That gives способный.

Compare:

• способная девушка = a capable girl
• способное решение = a capable/appropriate solution (neuter adjective form)
• способные инспекторы = capable inspectors

It is in the nominative case.

That is because the sentence is a present-tense identification/description sentence with no expressed is:

• Он = subject
• способный инспектор = predicate noun phrase

In simple present-tense sentences like this, Russian commonly uses the nominative:

• Он врач
• Она учительница
• Он способный инспектор

A useful contrast is the past tense, where the instrumental is very common:

• Он был инспектором
• Он был способным инспектором

So for this sentence as written, nominative is what you expect.

Russian has no articles like a/an or the.

So инспектор can mean:

• an inspector
• the inspector

The context tells you which one is meant.

In a neutral sentence like Он способный инспектор, English will usually translate it as He is a capable inspector.

If the context clearly points to a specific inspector, English might use the instead.

Yes, but it is not exactly the same.

• Он способный инспектор = He is a capable/talented inspector
• Он способен = He is capable

The form способный is the full adjective. Here it describes the noun инспектор.

The form способен is the short adjective. It is often used predicatively, especially when followed by an infinitive or another complement:

• Он способен помочь = He is capable of helping
• Он способен на многое = He is capable of a lot

So in your sentence, способный is the natural form because it goes with the noun инспектор.

Because with a personal pronoun like он, Russian normally does not use a dash in a plain neutral sentence of this type.

So:

• Он способный инспектор is normal

You may see a dash if the speaker wants extra emphasis, contrast, or a pause:

• Он — способный инспектор, но слишком доверчивый
• Он — не просто инспектор, а очень способный инспектор

But without special emphasis, no dash is the standard choice.

Yes, Russian word order is flexible, but the neutral order here is:

• Он способный инспектор

That is the most straightforward way to say it.

If you change the order, the basic meaning may stay similar, but the emphasis changes. For example:

• Он способный инспектор = neutral statement
• Способный инспектор — он = marked, emphatic, poetic, or contrastive
• Инспектор он способный = conversational, with emphasis on capable

For a learner, the best version to use is the original one: Он способный инспектор.

In Russian, nouns ending in a consonant are very often masculine.

инспектор ends in -р, so it is masculine.

That is why the adjective is also masculine:

• способный инспектор

This matches the pronoun он, which is also masculine.

So the whole sentence is grammatically consistent:

• он — masculine
• способный — masculine
• инспектор — masculine

Grammatically, способный is describing инспектор inside the noun phrase способный инспектор.

So the structure is:

• Он = subject
• способный инспектор = predicate noun phrase

In other words, the sentence means He is [a capable inspector], not He is capable, inspector.

This matters because it explains why the full adjective способный is used: it belongs to the noun инспектор.