Constipation is a common symptom of untreated or under-treated hypothyroidism. Your partner's thyroid test results show under-medication to me.
Serum Free T4 15.5 (12 - 22) ** 35% of the way through the reference range **
Serum Free T3 3.2 (3.1 - 6.8) ** 3% of the way through the reference range **
Most people who are hypothyroid and are being treated for it feel best when Free T4 and Free T3 are in the upper half of the range, and some need them to be in the upper third or even the upper quarter of the range to feel well. Where someone feels well is an individual thing, but I haven't come across a single person who feels best with Free T4 and Free T3 in the lower half of the range or right at the bottom of the range.
To get an idea of what TSH looks like for healthy people with no history of thyroid disease, take a look at this graph :
If you read the blurb you can see that the median result for TSH was 1.50 and the mode was 1.25, both being substantially lower than your partner's result.
The data for the graph was gleaned from this research paper :
My favourite part of that paper is the right hand half of Table 3 which shows the median TSH for each gender in different age groups. So, for example, in healthy women with no history of thyroid disease, aged 40 - 49 (for example), the median TSH was 1.40.
People with hypothyroidism generally feel best with a TSH lower than that of healthy people, so should aim for a TSH of 1 or under, so your partner definitely needs more medication.
If your partner has been supplementing but her nutrient levels aren't improving you should post her blood test results for vitamins and minerals and also let us know what she has been supplementing. It could be she needs a different type of supplement or the dose is insufficient to raise levels.