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Dip your trowel into the mortar to scoop up a small coating. Spread about 1⁄2 in (13 mm) of mortar over the left and right sides of the cavity. Finish by coating the bottom of the hole with an equal amount of mortar. If the mortar begins drying out while you're mixing and applying more mortar, lightly moisten it with a hose or misting bottle. Add another ½ inch layer of mortar to the brick's top. Even and smooth out the mortar before putting the brick in place. Pick up the brick and push it into the hole. Mortar will ooze out, so make sure you're still wearing sturdy gloves. Use the trowel or a tuckpointing tool to catch the oozing mortar and push it back into the spaces around the brick. Load more mortar onto one of these tools and push it into these joint spaces until they're full. After you've finished filling the joints, stroke a flat blade over the mortar to even it out. In addition to the trowel or tuckpointing tool, you may use a brick jointer. Blend in your work by making it match the joints around other bricks as much as possible. Let the joint mortar set up until it just gives when you press your finger into it, and then use the brick jointer tool to create the dimpled beveled joint lines. If the mortar is too wet when you create the beveled joint lines, then it may just scrape out of the joints. Use the brush to remove any mortar that has spilled over the bricks. Dampen the mortar first if it has begun to solidify. It's important to do this immediately or else you'll need muriatic acid or a commercial cleaner to remove the mortar. Take special care when using muriatic acid. Fill a spray bottle with water and immediately use it to lightly mist the new mortar today. This allows the mortar to cure properly. Do this once a day until the mortar is strong. Purchase a tarp and tape it over the new mortar right after you've misted it the first time. The tarp keeps the mortar safe from the sun and rain. You will need to pull down the tarp to mist the mortar, but after 72 hours it should be safe to remove permanently.

Summary:
Spread a layer of mortar inside the hole. Cover the top of the brick in mortar. Slide the brick into the hole. Fill the joints with mortar. Smooth out the mortar to match the rest of the wall. Wipe away excess mortar with a soft-bristle brush. Spray the mortar daily for 3 days. Cover the mortar when you're not misting it.