Hi, thanks for your query.
From your description of a flat lesion, not changing in size, no associated symptom and appearance of another one close to it, it seems that your partner has developed warts
Warts are due to a viral infection and are contagious. They can be easily treated by minimally invasive procedure like electro or radio cautery in a clinical setting.
Other thing may be seborrhoeic keratosis
or even a carcinomatous growth.
You may consult a dermatologist
for exact diagnosis and treatment. A skin biopsy
may be done if diagnosis is clinically difficult.
Hope this helps you. You may write back if you have any doubts.