First steps are logical: Bring F to the top-right corner, G to the bottom to make space and bring the small block (K) out from underneath E:

Next, bring the horizontal blocks (A, B) to the right of F allowing you to move G temporarily and rescue K out of its corner:

Bring H to the right underneath F to create shuffling space in the top left:

Now bring a horizontal block (B) between H and F:

Next we can stack the vertical blocks (C, E) as well as H to the left to allow more shuffling on the right:

Bring H to the bottom left (this one is quite tricky):

And slowly walk F to the left:

Bring a horizontal block (A or B) into the top right corner:

Now we can bring G all the way to the bottom right corner, giving us space to move the vertical and horizontal blocks around:

Bring a horizontal block (A or B) underneath G:

F back to the right and vertical blocks top left:

Now we can finally get H to the right and out of the way:

From here, it gets easy to start marching G to the left and up:

To get G up the final step, we still need to get the vertical blocks out. Bring H down and F back to the top right:

...and route G over the top to its destination: