An elf receives the benefits of a long rest in 4 hours while using the "Trance" trait.

According to the 2017 update to the Sage Advice Compendium:

Q: Does the Trance trait allow an elf to finish a long rest in 4 hours?

A: If an elf meditates during a long rest (as described in the Trance trait), the elf finishes the rest after only 4 hours. A meditating elf otherwise follows all the rules for a long rest; only the duration is changed. This answer has been altered as a result of a tweak to the rules for a long rest, which appears in newer printings of the Player’s Handbook.

This ruling reverses guidance in the earlier version of the SAC, due to errata changing the rules for long rests.

Interactions between the "Trance" trait and long rests

A long rest is defined as:

... a period of extended downtime, at least 8 hours long, during which a character sleeps for at least 6 hours and performs no more than 2 hours of light activity, such as reading, talking, eating, or standing watch.

The elf's Trance trait is defined as:

Elves don’t need to sleep. Instead, they meditate deeply, remaining semiconscious, for 4 hours a day. (The Common word for such meditation is “trance.”) While meditating, you can dream after a fashion; such dreams are actually mental exercises that have become reflexive through years of practice. After resting in this way, you gain the same benefit that a human does from 8 hours of sleep.

Since the "Trance" trait replaces the need for sleep (which most races need in order to complete a long rest), the elf is able to satisfy the requirements of the long rest while in a semiconscious trance for four hours.

It should be fine, as long as time allows.

Nothing in the rules says that a long rest cannot immediately follow a short rest. In this case, what the characters are doing during those rests are very different.

Indeed, a short rest and a long rest are what many real-life people do before bed: an hour or so of non-strenuous activity, like reading, and then going to sleep. It's not a stretch to say that a D&D character can't spend an hour studying their magical item, and then go to sleep.

The only time where that might be a problem is if the characters don't have the full 9 hours.

Different things are happening during the two rests.

What's really key here is that the activities during the two rests are different. In the short rest portion, the character is studying the magic item, meditating on it, or whatever is required for attunement. In the long rest portion, the character is doing something else, such as sleeping. The attunement process is still active work, just not active relative to adventuring.

I think that this distinction is why attunement is limited to short rests, and why a character should be able to do chain them together.