Select Tab "Pose/Animate"

In "Pose/Animate": Select Tab "Skeleton"

Select Rig Preset "Game Engine"

Select Tab "Files"

In "Files": Select Tab "Export"

Select Mesh Format: Filmbox (fbx)

Select Scale Unit: centimeter

Click "Export"

On source file change detection: Click "Import" (in upcoming Window "Import all")

Open imported Skeletal Mesh

Open Skeleton Editor

Click "Retarget Manager"

Open Drop Down "Select Rig"

Select "Select Humanoid Rig"

Click "Save Pose" (Bones from MH are named same as the ones in UE => no change needed)

Open Animation you want to retarget

Open Skeleton Editor

Click "Retarget Manager"

Open Drop Down "Select Rig"

Select "Select Humanoid Rig"

Click "Save Pose"

Right Click Animation you want to retarget

Select "Retarget Anim Asset" => "Duplicate Anmim Assets and Retarget"

Select your target Skeleton

Click "Retarget"

Open the new Anim Asset next to your target Skeleton

There might be Glitches in the Animation. To fix them:

Open Skeleton Editor

Make sure Box next to "Show Advanced Options" is checked

Right click the "Root" bone of your Skeleton (or the broken one itself if you want to go step by step)

Click "Recursively Set Translation Retargeting Skeleton" in upcoming menu

The final result without Glitches