Is marriage to a woman who converted to Islam after her first marriage, and did not obtain a divorce certificate from her former husband who abandoned her four years ago, permissible and valid according to the Sunnah of Allah and His Messenger?

It is not permissible to marry a married woman or a woman in her 'iddah (waiting period). If a man marries her, the contract is invalid and must be annulled. The child born from this corrupt marriage is attributed to him by lineage if he was unaware of the Shariah ruling.