"I have ideas in mind (such as shifting the dest 13 bits left and use bit operations)"

On an 8-bit processor, that doesn't sound like a very good idea! ;-)

"I think there should be better C-solutions."

Unlikely - 'C' has no native support for bit operations!

I think you should look at rotating out of the 1st bitstream into the carry bit, and then rotating that into the 2nd bitstream...