Firstly I'm very sorry for your loss and please accept my condolences.
You ask a complex question and I will try to be gentle about it and explain very thoroughly. I am not a doctor but I've been ill now for 15 years. This information is not professional advice but simply my insight into the issues you raise. I'm old fashioned so I write in sentences not text speak. So this is long I hope you don't mind.
Firstly the endocrinologist's specialism may not be an issue. They may in fact be very well informed however they could not give you any other answer on these test results.
The TPO test or thyroid peroxidase is outside range showing antibodies in the system although results much higher than 81 iU/L are possible. The level should be <35 so the result shows an autoimmune antibody. This result would indicate a thyroid problem. This test was done to check for a common reason for the other two test results which are out of range. But this test is not definitive - there are a range of antibody tests which would have been needed to identify the root cause of the thyrotoxicosis. Approximately 90% of all thyrotoxicosis conditions (that are autoimmune) come from Graves Disease or a subacute version although there are 11 conditions in total. This is why the TPOab test is not definitive just an indicator pointing in the autoimmune direction.
Thyrotoxicosis is a group heading referring to the clinical effects of unbound thyroid hormones, whether or not the thyroid gland is the primary source. But if the problem is in the thyroid it is a primary thyroid problem and the TPOab would indicate thyroid. If it was elsewhere like the pituitary affecting thyroid then it would be a secondary thyroid problem. That's all this means. Hyperthyroidism is not the same as thyrotoxicosis although the terms are often used interchangeably. The reason is the mechanism of 'overdose' of thyroid. Hyperthyroidism refers to overactivity of the thyroid gland, which leads to excessive release of thyroid hormones and consequently accelerated metabolism in the peripheral tissues and this faster working is not the same as too much free hormone levels in the blood.
A Free T4 range (and please bear in mind this changes with both Lab and country but it's generally close) is normally 10 - 23 pmol/L (although it can rise to 25pmol/L). Your husband's result is 25.8 which is a reduction on his previous result of 30.3. He is just above normal range. What this means is he has an elevated amount of hormone in his blood - thyrotoxicosis. To note here the higher the number the faster your body's systems work but this number can get much higher than 25.8 or even 30.3 therefore this is mild but it is still a problem.
The TSH test is how much thyroid stimulating hormone is released (which triggers the T4 some of which is bound and a tiny bit is unbound (Free-T4). TSH is triggered by the pituitary gland (as part of a pituitary, thyroid, hypothalamus loop). But when antibodies are present this system can be affected because the antibodies can attack the thyroid causing it to do too much or too little. Normal TSH is 0.5 - 4.70 µIU/mL although some labs have this lower figure as 0.3. Your husband's results are: 0.01 in both tests - which is a clear hyper result. To note here the lower the figure the faster your body's systems work. This figure indicates hyperthyroidism but as F-T4 is more important this takes precedence in diagnosis hence mild thyrotoxicosis (probably brought on by some kind of autoimmune action) BUT if the TSH had been in a normal range it could not have been thyrotoxicosis so for this condition to be diagnosed at all the TSH result is critical. Without further tests this cannot be narrowed further.
Treatments for the identified condition often include drugs such as anti-thyroids to reduce the production of thyroid hormone. It's a point to note that raising the TSH should have reduced his hypertension if it was caused by his hyperthyroidism and/or alleviated other heart strains which are common with hyperthyroidism even though you don't mention any specifically. This is an excellent link you may want to look at: bestpractice.bmj.com/best-p... which looks at study outcomes on thyroid issues or this more detailed one medscape.com/viewarticle/45... which gives more detail on TSH etc.
Therefore the result of mild thyrotoxicosis would seem correct on this data (possibly from an autoimmune cause). But this diagnosis does not provide a reason for someone to pass away unless it can be proved to have triggered something like heart disease, diabetes or a lethal stroke etc. I hope my explanation has helped you know why this very basic result was given and why nothing else could be offered from just these tests?
Please do accept my best wishes to you during this difficult time.