How to translate/use 一巧
The typo aside, there are a few grammatical issues with your sentence.


(Mis)use of the 尽管...可是... construction. This conjunctional
construction, like in English (even though/notwithstanding),
indicates a condition/status, preceded by 尽管 and a second condition
that indicates a contrast to the first, usually indicated by
adverbs like 却, 但还是, 也要, and very rarely, 可是. In your example, the
second condition seems to be a complementary/favourable condition to
the first or simply a statement, rather than a contrast.
The phrase 我一巧也开始喜欢它 makes no sense at all. My guess is that you
are simply trying to tell people that '一巧' (whoever that is) also
started to love the album. 开始喜欢 is grammatically sound in Mandarin
(assuming this is the flavour of Chinese you are learning), but it
does sound a little awkward to my ears. A better way to express this
would be 渐渐地喜欢上. I am not certain what you are trying to describe with 我一巧, but if you insist on using this structure, then might I suggest 我的一巧. 我的一巧 (my 一巧) is used to indicate a very intimate relationship between you and 一巧, to the extent of a romantic relationship. I can only assume that 一巧 is male, because you used the pronoun (他) in the second sentence (even though it sounds more female than male). 
Lastly, this should really be split into two sentences


Here is my attempt at reconstructing the sentence and my take on its meaning:


  我很喜欢这张唱片，就连我的一巧也渐渐地在喜欢上它。 想到以后可以跟一巧一起听音乐，我决定把这张唱片给他。
  
  I really love this album; even my yiqiao is beginning to like it. Realizing that I can listen to music together with yiqiao from now on, I decide to give this album to him.