Your breadboard is missing the connectors and (as you noted) the layer ids. Your best bet is to start with an existing part (in this case either a similar power supply or a generic IC with 6pins. Doing that will get you the necessary layer ids and connectors to move around in the svg editor of your choice. I'll clone something and upload a better part in a bit.
edit: OK its a bit later now. Below is a mostly working part as an example. I used copy / paste on breadboard to copy in 6 appropriate terminals from one of my other parts (DC 3.3v-10v TO ± 12V Mini DC converter.fzpz, posted here earlier). I changed the font from arial (which fritzing doesn't support) to OCRA, but fritzing apparantly doesn't like the tspan text either. You will need to find a working part breadboard and adjust the text xml til fritzing is happier. For schematic (and to create the fzp file) I used a generic 6 pin ic and modified the schematic. Feel free to move it around if you don't like it. For pcb I copied in the pcb svg from the converter and changed the text so the pads match the connections in the fzp. You will need to move the pads and silkscreen around (leaving the grouping as is) to match the real board. To get the fzp and svg files just unzip the .fzpz file below (I use 7zip). If you have questions or problems please post. Note it is most useful to upload the fzpz file for the part (7th button from the left in the reply menu) as then we get all the files to look at.
tp4056.fzpz (12.8 KB)
downloading this and loading it with the file open command in fritzing will get you a semi working part.
Peter