Después de haber mostrado el documento en la ventanilla, pude entregar el formulario.

Both are possible, but they are not exactly the same.

• Después de mostrar el documento... = after showing the document
• Después de haber mostrado el documento... = after having shown the document

The form haber + past participle (haber mostrado) is the perfect infinitive. It makes it especially clear that the first action was fully completed before the second one happened.

In everyday Spanish, después de mostrar is often enough, and many native speakers would say it.
Using después de haber mostrado sounds a bit more explicit, and sometimes a bit more formal or careful.

So in this sentence, it highlights the sequence:

1. first, the document was shown
2. then, the form could be handed in

Haber mostrado is the perfect infinitive.

It is made with:

• haber
  • past participle

Here:

• haber = infinitive of the auxiliary verb
• mostrado = past participle of mostrar

This structure is used when you want an infinitive phrase to refer to an action that happened before another action.

Examples:

• Después de comer = after eating
• Después de haber comido = after having eaten

The second version stresses prior completion more clearly.

Both mostrar and enseñar can mean to show, but mostrar fits better here.

With documents in official situations, Spanish often uses:

• mostrar un documento = to show/present a document

Enseñar can also mean to show, especially in casual speech, but it is also very commonly to teach. Because of that, mostrar sounds more precise and natural in administrative or formal contexts.

So:

• mostrar el documento = very natural here
• enseñar el documento = understandable, but less formal/less typical in this context

La ventanilla literally means little window, but in this kind of sentence it usually means a service window, ticket window, or counter window in an office, station, bank, government building, etc.

So en la ventanilla means something like:

• at the service window
• at the counter window
• at the clerk’s window

In Spain, ventanilla is very common in bureaucratic and administrative contexts.

This is a very common learner question, because both can translate as I could in English, but they do not mean the same thing.

• pude entregar = I managed to hand in / I was able to hand in
• podía entregar = I could hand in / I was allowed to hand in / I was able to hand in in a more general or ongoing sense

Here, pude is the preterite of poder, and it usually points to a specific completed moment. It often suggests that the action was actually achieved.

So this sentence implies:

• after showing the document, I was then able to hand in the form
• and in context, I probably did hand it in

If it said podía entregar, it would sound more like describing a general possibility or situation, not the successful completion of a specific event.

Usually, yes.

In many contexts, poder in the preterite (pude, pudo, pudimos, etc.) often suggests managed to or succeeded in being able to do something.

So:

• Pude entregar el formulario often implies I managed to hand in the form

That said, context always matters. But in a sentence like this one, the normal interpretation is that the action really happened.

Because Spanish usually does not need subject pronouns when the verb ending already shows the subject.

Here:

• pude clearly means I could / I managed to

So yo is unnecessary unless the speaker wants emphasis or contrast.

Compare:

• Pude entregar el formulario. = normal, neutral
• Yo pude entregar el formulario. = I was able to hand it in (perhaps unlike someone else)

Spanish is a pro-drop language, so leaving out subject pronouns is very common.

Spanish uses definite articles much more often than English.

Here, el documento and el formulario refer to specific things known in the situation:

• the document that had to be shown
• the form that had to be handed in

So Spanish naturally says:

• mostrar el documento
• entregar el formulario

Even when English might sometimes say show document in note-like or instructional language, normal Spanish usually wants the article in full sentences.

Entregar is very natural here because it means to hand over, to submit, or to hand in.

In an administrative context:

• entregar un formulario = to hand in/submit a form

Other verbs are possible, but with different nuances:

• dar = to give
  
  • grammatically possible in some contexts, but too general here
• presentar = to submit/file/present formally
  
  • also possible, often a bit more official

So:

• entregar el formulario = very natural
• presentar el formulario = also possible, perhaps slightly more formal/bureaucratic
• dar el formulario = understandable, but less idiomatic in this context

Yes.

Spanish allows several word orders here. For example:

• Después de haber mostrado el documento en la ventanilla, pude entregar el formulario.
• Pude entregar el formulario después de haber mostrado el documento en la ventanilla.

Both are correct.

Starting with Después de... puts the sequence first and sounds very natural.
Also, the comma is normal when the sentence begins with that introductory time clause.

Yes, but the structure changes.

Use después de + infinitive when the subject is the same:

• Después de haber mostrado el documento, pude entregar el formulario.

This means the same person showed the document and then handed in the form.

Use después de que + finite verb when you want an explicit subject, especially if the subject is different:

• Después de que el empleado revisó el documento, pude entregar el formulario.
• Después de que mostré el documento, pude entregar el formulario.

That is also correct, but in your original sentence the infinitive structure is more compact and very natural because the subject is understood to be the same person.

It sounds fairly neutral to slightly formal, mainly because of the context and the structure.

Reasons it feels a bit formal:

• administrative vocabulary like documento, ventanilla, formulario
• the use of después de haber mostrado, which is slightly more elaborate than después de mostrar

This is the kind of sentence you might hear or read in official, bureaucratic, or narrative contexts. It is not unnatural in conversation, but it is not especially casual either.

A more everyday version could be:

• Después de mostrar el documento en la ventanilla, pude entregar el formulario.

That sounds a bit simpler while keeping the same meaning.