When do you receive the bonus for increasing friendship level?

When you open their gift, they open your gift or you two battle/raid together.

When someone opens the gift, dont need to both open.
If there's a blue in your friend`s picture, your friendship already leveled that day.

Small Caveat to this answer: This was true a month ago, the last time I actually did this. I haven't heard of it changing since then.

When a Gift is opened by either Friend, the Bonus is available to BOTH accounts... with a small but important lag. It won't be APPLIED to the accounts until after the Bonus Screen pops up. (The black overlay that says "Yay! You've Leveled up a Friendship with Friend X! Here's your new Bonuses and your XP Bonus notification!" is what I'm talking about here.) This is vitally important if you've forgotten to put on a Lucky Egg.

So let's say that at 10am, you open a gift from a friend and your friendship level increases. After you close the Friends screen, there will be a few seconds pause and then the Friendship Increased screen will come up. BUT you forgot to put on a Lucky Egg. You have that few seconds (maybe 3 seconds) between closing the Friends Screen and the Bonus popping up where you can tap the Pokeball, go into your Items, put on a Lucky Egg and still get the effects of the Lucky Egg.

Say your friend opens their Pokémon Go at 1pm (3 hours after you opened their Gift), they will get the XP Bonus applied at that time - NOT at the 10am when you opened it. The bonus is waiting on their account, but won't be finally processed until they've opened up their game. Your friend has a few seconds from when he opens the App to when their Bonus screen pops up (depends on how many updates; it seems like the Friendship Bonus screen is a priority notification, so your Friend might have that same 3-ish seconds from the time of opening the App to get to the Items Screen) to put on a Lucky Egg for themselves, just like how you had a few seconds between opening the gift and getting the XP bonus.

In other words, if you forgot to coordinate with your Friend to put on a Lucky Egg, they can still get the XP bonus - they just need to immediately put on a Lucky Egg once they open the App for the first time after you opened the Gift. And it's dependant on that Friendship Bonus Increase screen coming up - you have 3-ish seconds to open the Items screen, then a few more seconds to open a Lucky Egg. I've never tried to see how long before the Bonus is applied to the account anyway, but I wouldn't recommend delaying any more than you absolutely have to. (I also don't know if you could buy a Lucky Egg and apply it before the Bonus overlay came up, and the XP Bonus was applied.)