You need to find a file format that is compatible between both softwares, regarding Ansys output and Abaqus inputs.
There may be some Ansys module to make conversions, or you can also write in the apdl a code to create the corresponding Abaqus file.
If you have MATLAB the SDT FEMLink toolbox is another tool that will allow you to import Ansys models into SDT then export to Abaqus among many other finite element codes ( http://www.sdtools.com/femlink.html ).
Write out the nodes and element in txt or asci or IGES format in export of ANSYS... You may import them then in ABAQUS... but, coordinate system in both codes are different, hence you may view model looks like rotated
Professional solution - Hypermesh (www.altairhyperworks.com/)
This software allows
1) to correct many CAD formats (many softwares) in order to get them meshable.
2) create FEM file (meshing, loads, boundary conditions etc)
3) store FEM file in almost all available formats - ANSYS, ABAQUS, NASTRAN, LS-DYNA etc
4) check mesh quality (distortion, connectivity etc) - as an additional option - linear static and modal analysis
Your question is just a subtask from 3) --> take full FEM file from one format and store this in another format (e.g. ANSYS > ABAQUS)!!! But you need FEM file looking like (nodes, elements, nodal and surface loads etc)