It may be almost obvious but before spoiling the sensor I preferred to ask the questions and advise me, thanks for your opinion
Connecting a single winding is still 110 V working voltage but the power would be half. For another occasion when you are not sure, use an incandescent lamp connected in series and if everything is correct you have to turn on the filament very dim. If it turns on emitting a lot of light it indicates that the thing is wrong.
Thanks man I like to learn and expand my knowledge. I consider the issue resolved. by chance do you also know how reed switch works? I have another open question of a gems fs200 valve if you want we can analyze and share to see if it can be solved.