Yes and no, it's between 15 & 21 (not 16) which means he's eligible for the A list. He's not been here the required 2 years to make the B list.
43.04 A "club-trained player" is a player who, between the age of 15 (or the start of the season during which he turns 15) and 21 (or the end of the season during which he turns 21), and irrespective of his nationality and age, has been registered with his current club for a period, continuous or not, of three entire seasons (i.e. a period starting with the first official match of the relevant national championship and ending with the last official match of that relevant national championship) or of 36 months.
43.05 An "association-trained player" is a player who, between the age of 15 (or the start of the season during which the player turns 15) and 21 (or the end of the season during which the player turns 21), and irrespective of his nationality and age, has been registered with a club or with other clubs affiliated to the same association as that of his current
43.11 A player may be registered on List B if he is born on or after 1 January 1994 and has been eligible to play for the club concerned for any uninterrupted period of two years since his 15th birthday by the time he is registered with UEFA. Players aged 16 may be registered on List B if they have been registered with the participating club for the previous two years without interruption.
http://www.uefa.org/MultimediaFiles.../Regulations/02/23/57/51/2235751_DOWNLOAD.pdf
That was what I ment, I know for the b list he would have to be here for 2 years but at 19 should be able to go into our squad's a list